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Surface Area Worksheets

Surface area worksheets comprise an enormous collection of exercises on different solid figures. The large chunk of exercises is categorized based on a step-by-step approach involving counting unit squares to determine the SA, finding the surface area of nets, and then computing the surface area of geometrical shapes like cubes, cones, cylinders, rectangular prisms, L-shaped prisms, spheres, hemispheres, pyramids, and composite figures, catering to the needs of students in 5th grade through high school. Revisiting surface area is easy with our mixed 3D shapes revision pdfs. Count on our free printable SA worksheets for a great start!

List of Surface Area Worksheets

• Surface Area of 3D Figures Using Nets
• Surface Area by Counting Squares
• Surface Area of Cubes
• Surface Area of Rectangular Prisms
• Surface Area of L-Shaped Prisms
• Surface Area of Triangular Prisms
• Surface Area of Cylinders
• Surface Area of Prisms and Cylinders
• Surface Area of Cones
• Surface Area of Spheres and Hemispheres
• Surface Area of Pyramids
• Surface Area of Mixed Solid Shapes
• Surface Area of Composite Figures

Explore the Surface Area Worksheets in Detail

Surface Area of 3D Figures Using Nets Worksheets

Finding the surface area of 3D figures using nets worksheets assist students in visualizing the surface of solid shapes whose nets are sketched on grids. Add on to their practice in determining the SA of the nets of 3D shapes like cylinders, cones, and pyramids, and in drawing the nets of solid figures too.

Surface Area by Counting Squares Worksheets

Start off with counting unit squares on an isometric paper, follow up by drawing the correct number of squares, and then find the SA of rectangular prisms by counting the squares scaled to varied units. These interesting exercises make the surface area by counting squares pdfs a compulsive print for your grade 5 and grade 6 students.

Surface Area of Cubes Worksheets

Page through these surface area of a cube exercises to practice computing the total area occupied by the cubes with edge length offered as integers, decimals and fractions. Included here are pdfs to find the missing edge length using the SA and more.

Surface Area of Rectangular Prisms Worksheets

Surface area of rectangular prisms handouts are a sure-fire hit in every grade 6, grade 7, and grade 8 geometry curriculum. Find the SA using the height, width, and length, and extend your practice to finding the missing dimensions as well.

Surface Area of L-Shaped Prisms Worksheets

Lay a strong foundation in decomposing shapes with these printable surface area of L-shaped rectangular prism worksheets. Solve for surface area of independent 3D shapes, add them, and subtract the area of the face that connects the rectangular blocks.

Surface Area of Triangular Prisms Worksheets

Expedite practice calculating the surface area of triangular prisms with these worksheet pdfs, rendering the attributes of the triangular bases and rectangular side faces of the figure, in integers and decimals.

Surface Area of Cylinders Worksheets

The surface area of a cylinder pdfs feature solid shapes, each made up of a curved surface with two circular bases. Recall the formula for SA of a cylinder, plug in the integer, decimal, or fractional radius measures in the formula 2πrh + 2πr 2 and compute.

Surface Area of Prisms and Cylinders Worksheets

A mix of rectangular prisms, triangular prisms, and cylinders is what these printable worksheets have in store for your middle and high school learners. Consider memorizing the SA formulas, apply the one relevant to the solid shape, substitute the dimensions and solve.

Surface Area of Cones Worksheets

Give your 6th grade, 7th grade, and 8th grade students an edge over their peers with these surface area of cones exercises. Supplying the values of the dimensions in the formula and calculating the surface area of cones is all that is expected of learners.

Surface Area of Spheres and Hemispheres Worksheets

Build fluency and competence with this collection of surface area of spheres and hemispheres worksheets. Get students to find the TSA of the hemispheres and CSA of the spheres by substituting the dimensions in relevant formulas.

Surface Area of Pyramids Worksheets

Handle these printable surface area of pyramid practice sheets with great dexterity. Learn the know-how of finding the surface area of pyramids applying relevant formulas and substituting the dimensions accordingly.

Surface Area of Mixed Solid Shapes Worksheets

How well do your 8th grade and high school students remember the SA formulas of solid shapes like cubes, cones, cylinders, spheres, hemispheres, prisms and pyramids? Check for yourself with these surface area of solid shapes revision pdfs.

Surface Area of Composite Figures Worksheets

Tee up to decompose each combined shape, find the sum of the SA of individual 3D shapes, subtract the area of the common parts, and determine the SA like a pro with this set of printable surface area of composite shapes worksheets.

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Surface Area Worksheet 6th Grade

Welcome to our Surface Area Worksheet 6th Grade collection.

Here you will find a range of surface area worksheets to help you learn how to find the surface area of a range of different nets including cubes, prisms and pyramids.

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Surface Area Support

• Surface Area of Cubes Worksheets
• Surface Area of Cuboids Worksheets
• Surface Area of Prisms and Pyramids Worksheets
• Surface Area Mixed 3D shapes Worksheets
• More recommended resources
• 6th Grade Surface Area Online Quiz

Surface Area Worksheet 6th Grade Collection

This page is all about finding the surface area of a range of different 3d shapes, drawn as nets.

The 3d shapes include:

• cubes and cuboids;
• triangular prisms;
• square pyramids.

Some of the sheets also involve working out the lengths of an unknown side, when the surface area is given.

Want to test yourself to see how well you have understood this skill?.

• Try our NEW quick quiz at the bottom of this page.

What is the surface area of a 3d shape?

The surface area of a 3D shape is the sum of the areas on all of the outer faces.

How to find the surface area of a 3d shape?

To find the surface area of a 3d shape, we need to find the area of each of the faces.

To find the area of square and rectangular faces, we just need to multiply the adjacent sides together.

To find the area of triangular faces, we need to multiply the base by the perpendicular height and then halve the answer.

Example 1) Find the surface area of the cube below.

The width of one side of each square face is 4cm.

So the area of each square face is 4 x 4 = 16 cm 2 .

The cube has 6 identical square faces, so the total surface area is 16 x 6 = 96 cm 2 .

Example 2) What is the surface area of the cube below.

The width of one side of each square face is 1 ½ inches.

So the area of each square face is 1 ½ x 1 ½ = 2 ¼ in 2 .

The cube has 6 identical square faces, so the total surface area is 2 ¼ x 6 = 13 ½ in 2 .

Example 3) Find the surface area of the cuboid below.

There are 6 faces in the cuboid, with 3 identical faces each repeated twice.

Face1: 6cm by 4cm. Area = 6 x 4 = 24 cm 2

Face2: 6cm by 3cm. Area = 6 x 3 = 18 cm 2

Face3: 3cm by 4cm. Area = 3 x 4 = 12 cm 2

The surface area of the cuboid is (Area of Face1 x 2) + (Area of Face2 x 2) + (Area of Face3 x 2)

So the surface area of this cuboid is (24 x 2) + (18 x 2) + (12 x 2) = 48 + 36 + 24 = 108 cm 2 .

Example 4) What is the surface area of the triangular prism below.

The triangular prism has 5 faces, two identical triangular faces, and three rectangular faces, two of which are identical.

Face1 (rectangular): 10 in by 5 in. Area = 10 x 5 = 50 in 2

Face2 (rectangular): 10 in by 6 in. Area = 10 x 6 = 60 in 2

Face3 (triangular): 6 in base and 4 in perpendicular height. Area = ½ x 6 x 4 = 3 x 4 = 12 in 2

So the surface area of the triangular prism is (Area of Face1 x 2) + Area of Face2 + (Area of Face3 x 2).

So the surface area is (50 x 2) + 60 + (12 x 2) = 100 + 60 + 24 = 184 in 2 .

Example 5) Find the surface area of the square pyramid below.

The square pyramid has one square face and four identical triangular faces.

Square Face: 12cm by 12cm. Area = 12 x 12 = 144 cm 2

Triangular Face: base: 12 cm perpendicular height: 8 cm. Area: ½ x 12 x 8 = 6 x 8 = 48 cm 2

The surface area of the pyramid is (Area of Square Face) + (Area of Triangular Face x 4)

So the surface area of this pyramid is 144 + (48 x 4) = 144 + 192 = 336 cm 2 .

Surface Area Worksheets

Surface area worksheet 6th grade - cube worksheets.

These sheets involve working out the surface area of a range of cubes.

The first two sheets involve finding the surface area of the cubes.

The third sheet is harder and also involves finding the length of one side of the square face, when the surface area is given.

• Surface Area of Cubes Sheet 1
• PDF version
• Surface Area of Cubes Sheet 2
• Surface Area of Cubes Sheet 3

Surface Area Worksheet 6th Grade - Cuboid Worksheets

These sheets involve working out the surface area of a range of cuboids from their nets.

The first two sheets involve finding the surface area of the cuboids.

The cuboids in the 2nd sheet have fractional length sides.

The third sheet is harder and involves finding the length of one side of the cuboid, when the surface area and two of the other sides are given.

• Surface Area of Cuboids Sheet 1
• Surface Area of Cuboids Sheet 2
• Surface Area of Cuboids Sheet 3

Surface Area Worksheet 6th Grade - Square Pyramid Worksheets

These sheets involve working out the surface area of a range of square pyramids from their nets.

• Surface Area of Square Pyramid Sheet 1

Surface Area Worksheet 6th Grade - Triangular Prism Worksheets

These sheets involve working out the surface area of a range of triangular prisms from their nets.

• Surface Area of Triangular Prisms Sheet 1

Surface Area Worksheet 6th Grade - Mixed Worksheets

These sheets involve working out the surface area of a range of different 3d shapes from the sheets above.

Shapes covered: cubes, cuboids, square pyramids and triangular prisms.

• Mixed Surface Area Worksheets 1
• Mixed Surface Area Worksheets 2

Surface Area of Cubes Pyramids and Prisms Walkthrough Video

This short video walkthrough shows several problems from our Surface Area Cubes Prisms & PyramidsWorksheet 1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More 6th Grade Geometry Worksheets

Here is our range of 6th grade Geometry worksheets including area and perimeter worksheets.

• Area of Quadrilaterals

• Surface Area of a Box
• Area of Right Triangle
• Square Inside a Circle Area Support Page
• Coordinate Plane Worksheets (All 4 Quadrants)

Surface Area 6th Grade Online Quiz

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This quick quiz tests your knowledge and skill at finding the surface area of different 3d nets.

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Surface Area Worksheets

This page has worksheets for calculating the area of rectangular prisms and other solid shapes.

Level: Basic (Rectangular Prisms & Cubes Only)

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Quickly access your most used files AND your custom generated worksheets!

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Level: Intermediate

Level: advanced (cylinders, triangular prisms, spheres).

Find the area of squares, rectangles, triangles, and circles. Includes basic, intermediate, and advanced-level worksheets.

Learn to solve operations in order: parenthesis, exponents, multiply & divide, add & subtract.

This page has geometry activities related to circles. Pupils find the area, circumference, radius, and/or diameter.

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Surface Area of a Cuboid

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Volume & surface area of rectangular prisms

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Geometry worksheets: Volume & surface area of rectangular prisms

Students calculate the volume and surface area of rectangular prisms . Answers should be expressed in the appropriate units . These worksheets are printable pdf files.

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Surface Area Worksheet

FREE DOWNLOAD

Give your grade 6 to 8 students skills and applied questions on surface area.

• 15 questions in total; 10 skills questions and 5 applied questions.
• Answer key included with the related common core standard.
• Print off and share with your classes to support their learning.
• Covers ‘Geometry’: 6.G.A.4

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Unit Surface Area Homework 5

Unit Surface Area Homework 5 - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Name geometry unit 12 volume surface area, Surface area and volume, Table of contents, Measurement and data volume grade 5 formative assessment, Surface area word problems name, Find the lateral area of the, Surface areas of prisms, Surface area prisms cylinders l2es1.

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1. NAME GEOMETRY UNIT 12 VOLUME & SURFACE AREA

2. surface area and volume, 3. table of contents, 4. measurement and data: volume grade 5 formative assessment ..., 5. surface area word problems: name:, 6. find the lateral area of the prism., 7. 6.2 surface areas of prisms, 8. surface area: prisms & cylinders l2es1.

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8.3: Solve Geometry Applications- Volume and Surface Area (Part 1)

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Learning Objectives

• Find volume and surface area of rectangular solids
• Find volume and surface area of spheres
• Find volume and surface area of cylinders
• Find volume of cones

be prepared!

Before you get started, take this readiness quiz.

• Evaluate x 3 when x = 5. If you missed this problem, review Example 2.3.3 .
• Evaluate 2 x when x = 5. If you missed this problem, review Example 2.3.4 .
• Find the area of a circle with radius \(\dfrac{7}{2}\). If you missed this problem, review Example 5.6.12 .

In this section, we will finish our study of geometry applications. We find the volume and surface area of some three-dimensional figures. Since we will be solving applications, we will once again show our Problem-Solving Strategy for Geometry Applications.

Problem Solving Strategy for Geometry Applications

• Step 1. Read the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.
• Step 2. Identify what you are looking for.
• Step 3. Name what you are looking for. Choose a variable to represent that quantity.
• Step 4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
• Step 5. Solve the equation using good algebra techniques.
• Step 6. Check the answer in the problem and make sure it makes sense.
• Step 7. Answer the question with a complete sentence.

Find Volume and Surface Area of Rectangular Solids

A cheerleading coach is having the squad paint wooden crates with the school colors to stand on at the games. (See Figure \(\PageIndex{1}\)). The amount of paint needed to cover the outside of each box is the surface area , a square measure of the total area of all the sides. The amount of space inside the crate is the volume, a cubic measure.

Figure \(\PageIndex{1}\) - This wooden crate is in the shape of a rectangular solid.

Each crate is in the shape of a rectangular solid . Its dimensions are the length, width, and height. The rectangular solid shown in Figure \(\PageIndex{2}\) has length 4 units, width 2 units, and height 3 units. Can you tell how many cubic units there are altogether? Let’s look layer by layer.

Figure \(\PageIndex{2}\) - Breaking a rectangular solid into layers makes it easier to visualize the number of cubic units it contains. This 4 by 2 by 3 rectangular solid has 24 cubic units.

Altogether there are 24 cubic units. Notice that 24 is the length × width × height.

The volume, V, of any rectangular solid is the product of the length, width, and height.

We could also write the formula for volume of a rectangular solid in terms of the area of the base. The area of the base, B, is equal to length × width.

\[B = L \cdot W\]

We can substitute B for L • W in the volume formula to get another form of the volume formula.

\[\begin{split} V &= \textcolor{red}{L \cdot W} \cdot H \\ V &= \textcolor{red}{(L \cdot W)} \cdot H \\ V &= \textcolor{red}{B} h \end{split}\]

We now have another version of the volume formula for rectangular solids. Let’s see how this works with the 4 × 2 × 3 rectangular solid we started with. See Figure \(\PageIndex{3}\).

Figure \(\PageIndex{3}\)

To find the surface area of a rectangular solid, think about finding the area of each of its faces. How many faces does the rectangular solid above have? You can see three of them.

\[\begin{split} A_{front} &= L \times W \qquad A_{side} = L \times W \qquad A_{top} = L \times W \\ A_{front} &= 4 \cdot 3 \qquad \quad \; A_{side} = 2 \cdot 3 \qquad \quad \; A_{top} = 4 \cdot 2 \\ A_{front} &= 12 \qquad \qquad A_{side} = 6 \qquad \qquad \; \; A_{top} = 8 \end{split}\]

Notice for each of the three faces you see, there is an identical opposite face that does not show.

\[\begin{split} S &= (front + back)+(left\; side + right\; side) + (top + bottom) \\ S &= (2 \cdot front) + (2 \cdot left\; side) + (2 \cdot top) \\ S &= 2 \cdot 12 + 2 \cdot 6 + 2 \cdot 8 \\ S &= 24 + 12 + 16 \\ S &= 52\; sq.\; units \end{split}\]

The surface area S of the rectangular solid shown in Figure \(\PageIndex{3}\) is 52 square units.

In general, to find the surface area of a rectangular solid, remember that each face is a rectangle, so its area is the product of its length and its width (see Figure \(\PageIndex{4}\)). Find the area of each face that you see and then multiply each area by two to account for the face on the opposite side.

\[S = 2LH + 2LW + 2WH\]

Figure \(\PageIndex{4}\) - For each face of the rectangular solid facing you, there is another face on the opposite side. There are 6 faces in all.

Definition: Volume and Surface Area of a Rectangular Solid

For a rectangular solid with length L, width W, and height H:

Example \(\PageIndex{1}\):

For a rectangular solid with length 14 cm, height 17 cm, and width 9 cm, find the (a) volume and (b) surface area.

Step 1 is the same for both (a) and (b), so we will show it just once.

Exercise \(\PageIndex{1}\):

Find the (a) volume and (b) surface area of rectangular solid with the: length 8 feet, width 9 feet, and height 11 feet.

Exercise \(\PageIndex{2}\):

Find the (a) volume and (b) surface area of rectangular solid with the: length 15 feet, width 12 feet, and height 8 feet.

1,440 cu. ft

Example \(\PageIndex{2}\):

A rectangular crate has a length of 30 inches, width of 25 inches, and height of 20 inches. Find its (a) volume and (b) surface area.

Exercise \(\PageIndex{3}\):

A rectangular box has length 9 feet, width 4 feet, and height 6 feet. Find its (a) volume and (b) surface area.

Exercise \(\PageIndex{4}\):

A rectangular suitcase has length 22 inches, width 14 inches, and height 9 inches. Find its (a) volume and (b) surface area.

2,772 cu. in

1,264 sq. in.

Volume and Surface Area of a Cube

A cube is a rectangular solid whose length, width, and height are equal. See Volume and Surface Area of a Cube, below. Substituting, s for the length, width and height into the formulas for volume and surface area of a rectangular solid, we get:

\[\begin{split} V &= LWH \quad \; S = 2LH + 2LW + 2WH \\ V &= s \cdot s \cdot s \quad S = 2s \cdot s + 2s \cdot s + 2s \cdot s \\ V &= s^{3} \qquad \quad S = 2s^{2} + 2s^{2} + 2s^{2} \\ &\qquad \qquad \quad \; S = 6s^{2} \end{split}\]

So for a cube, the formulas for volume and surface area are V = s 3 and S = 6s 2 .

Definition: Volume and Surface Area of a Cube

For any cube with sides of length s,

Example \(\PageIndex{3}\):

A cube is 2.5 inches on each side. Find its (a) volume and (b) surface area.

Exercise \(\PageIndex{5}\):

For a cube with side 4.5 meters, find the (a) volume and (b) surface area of the cube.

91.125 cu. m

121.5 sq. m

Exercise \(\PageIndex{6}\):

For a cube with side 7.3 yards, find the (a) volume and (b) surface area of the cube.

389.017 cu. yd.

319.74 sq. yd.

Example \(\PageIndex{4}\):

A notepad cube measures 2 inches on each side. Find its (a) volume and (b) surface area.

Exercise \(\PageIndex{7}\):

A packing box is a cube measuring 4 feet on each side. Find its (a) volume and (b) surface area.

Exercise \(\PageIndex{8}\):

A wall is made up of cube-shaped bricks. Each cube is 16 inches on each side. Find the (a) volume and (b) surface area of each cube.

4,096 cu. in.

Contributors and Attributions

Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/[email protected] ."

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Unit 7: Area and perimeter

About this unit.

Area and perimeter help us measure the size of 2D shapes. We’ll start with the area and perimeter of rectangles. From there, we’ll tackle trickier shapes, such as triangles and circles.

Count unit squares to find area

• Intro to area and unit squares (Opens a modal)
• Measuring rectangles with different unit squares (Opens a modal)
• Measuring area with partial unit squares (Opens a modal)
• Creating rectangles with a given area 1 (Opens a modal)
• Creating rectangles with a given area 2 (Opens a modal)
• Find area by counting unit squares 7 questions Practice
• Find area with partial unit squares 7 questions Practice
• Create rectangles with a given area 4 questions Practice

Area of rectangles

• Transitioning from unit squares to area formula (Opens a modal)
• Finding missing side when given area (Opens a modal)
• Counting unit squares to find area formula (Opens a modal)
• Area of rectangles review (Opens a modal)
• Transition from unit squares to area formula 7 questions Practice
• Find a missing side length when given area 7 questions Practice
• Perimeter: introduction (Opens a modal)
• Perimeter of a shape (Opens a modal)
• Find perimeter by counting unit squares (Opens a modal)
• Finding perimeter when a side length is missing (Opens a modal)
• Finding missing side length when given perimeter (Opens a modal)
• Perimeter & area (Opens a modal)
• Perimeter and unit conversion (Opens a modal)
• Applying the metric system to perimeter (Opens a modal)
• Perimeter review (Opens a modal)
• Find perimeter by counting units 4 questions Practice
• Find perimeter when given side lengths 7 questions Practice
• Find a missing side length when given perimeter 4 questions Practice

Area of parallelograms

• Area of a parallelogram (Opens a modal)
• Area of parallelograms (Opens a modal)
• Area of parallelograms 4 questions Practice
• Find missing length when given area of a parallelogram 4 questions Practice

Area of triangles

• Area of a triangle (Opens a modal)
• Area of triangles (Opens a modal)
• Area of triangle proof (Opens a modal)
• Find base and height on a triangle 4 questions Practice
• Area of right triangles 4 questions Practice
• Area of triangles 7 questions Practice
• Find missing length when given area of a triangle 4 questions Practice

Area of shapes on grids

• Area of a triangle on a grid (Opens a modal)
• Area of a quadrilateral on a grid (Opens a modal)
• Areas of shapes on grids 4 questions Practice

Area of trapezoids & composite figures

• Area of trapezoids (Opens a modal)
• Area of kites (Opens a modal)
• Finding area by rearranging parts (Opens a modal)
• Area of composite shapes (Opens a modal)
• Perimeter & area of composite shapes (Opens a modal)
• Challenge problems: perimeter & area (Opens a modal)
• Area of trapezoids 4 questions Practice
• Area of composite shapes 4 questions Practice
• Area challenge 4 questions Practice

Area and circumference of circles

• Radius, diameter, circumference & π (Opens a modal)
• Labeling parts of a circle (Opens a modal)
• Radius, diameter, & circumference (Opens a modal)
• Circumference review (Opens a modal)
• Radius & diameter from circumference (Opens a modal)
• Area of a circle (Opens a modal)
• Area of circles review (Opens a modal)
• Area of a circle intuition (Opens a modal)
• Radius and diameter 7 questions Practice
• Circumference of a circle 4 questions Practice
• Area of a circle 7 questions Practice
• Area of parts of circles 4 questions Practice

Advanced area with triangles

• Area of equilateral triangle (Opens a modal)
• Area of equilateral triangle (advanced) (Opens a modal)
• Area of diagonal-generated triangles (Opens a modal)

Basic Math Examples

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