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Surface Area

Site: Saylor Academy
Course: GKT101: General Knowledge for Teachers – Math
Book: Surface Area
Printed by: Guest user
Date: Saturday, 12 April 2025, 7:23 AM

Description

The boundary of three-dimensional objects consists of several two-dimensional shapes. The total area of these shapes is called the surface area of the object. It gives some idea of how large an object is, but now how much space it takes up. This is measured by volume, which we will discuss next. Watch this lecture series and complete the interactive exercises to practice calculating the surface area of rectangular prisms.

Table of contents

Surface area using a net: triangular prism

Surface area using a net: rectangular prism

Surface area of a box (cuboid)

Surface area of a box using nets

Surface area word problem example

Practice

    

Nets of polyhedra - Questions

1. Identify the net that corresponds to the figure below.



Choose 1 answer:


2. Identify the shape that can be formed using the following net.



Choose 1 answer:








3. Identify the net that corresponds to the figure below.



Choose 1 answer:


4. Identify the shape that can be formed using the following net.



Choose 1 answer:








Nets of polyhedra - Answers

1. The correct net is:



2. The correct answer is:



3. The correct net is:



4. The correct answer is:


Surface area using nets - Questions

1. Check out this square pyramid:


Find the surface area of the square pyramid (above) using its net (below).


__________ unit^{2}

2. Check out this triangular prism:



Find the surface area of the triangular prism (above) using its net (below).



__________ unit^{2}

3. Check out this cube:



Find the surface area of the cube (above) using its net (below).


__________ unit^{2}

4. Check out this rectangular prism



Find the surface area of the rectangular prism (above) using its net (below).



__________ unit^{2}

Surface area using nets - Answers

1. The surface area of this square pyramid is 12 units^{2}.

2. The surface area of this triangular prism is 96 units ^{2}.

3. The surface area of this cube is 54 units ^{2}.

4. The surface area of this rectangular prism is 48 units ^{2}.

Expressions to find surface area - Questions

1. The following figure shows a square-based pyramid.



Which expression represents the surface area of the pyramid?

Choose 1 answer:

(A) 100+80+80+80+80

(B) 10 \cdot 8

(C) 40 \cdot 4

(D) 100+40+40+40+40

2. The following figure shows a cube.



Which expression represents the surface area of the cube?

Choose 1 answer:

(A) 8+8+8+8+8+8

(B) 6 \cdot 16

(C) 6 \cdot 4

(D) 4 \cdot 4 \cdot 4

3. The following figure shows a right triangular prism.



Which expression represents the surface area of the prism?

Choose 1 answer:

(A) 2 \cdot 24+120+160+200

(B) 48+48+120+160+200

(C) 200+160+120+24

(D) 24+24+200+120+120

4. The following figure shows a right rectangular prism.



Which expression represents the surface area of the prism?

Choose 1 answer:

(A) 15+15+30+30+18

(B) 2 \cdot 15+2 \cdot 30+2 \cdot 18

(C) 6 \cdot 5 \cdot 3

(D) 6.5

Expressions to find surface area - Answers

1. Finally, we add the area of all 5 faces. The surface area of the rectangular prism can be found with the following expression:

100+40+40+40+40

2. There are six square faces with an area of 16 square units each. The following expression represents the surface area of the cube.

6 \cdot 16

3. Finally, we add the area of all 5 faces.

24+24+120+160+200

The following expression represents the surface area of the triangular prism.

2 \cdot 24+120+160+200

4. Finally, we add the area of all 6 faces.

15+15+30+30+18+18

The following expression represents the surface area of the rectangular prism.

2 \cdot 15+2 \cdot 30+2 \cdot 18

Surface area - Questions

1. Shaun's tent (shown below) is a triangular prism.



Find the surface area, including the floor, of his tent.

_______ m ^{2}

2. Find the surface area of the cube shown below.



_______ m ^{2}

3. Marie made a model (shown below) of the square pyramid she plans to build when she grows up.


Find the surface area of the model.

_______ m ^{2}

4. The cereal box shown below is a rectangular prism.



Find the surface area of the cereal box.

________ cm ^{2}

Surface area - Answers

1. The surface area of the tent is 52.8 m2.

2. The surface area of the cube is \frac{75}{2} units2.

3. The surface area of the square pyramid is 336 m2.

4. The surface area of the cereal box is 1,700 cm2.

Surface area word problems - Questions

1. A group of students made trees out of paper for a scene in a school play. The trees are shaped like hollow square pyramids.



They created this net to represent the paper they needed per tree.



How much paper will it take to make each tree, including the bottom?

_________ cm2

2. Dmitri's mom is making him a tent to use for backyard camp outs with his friends.


She created this net to represent the material she needed.



How much material will Dmitri's mom need for the tent, including the floor?

Give an exact answer (do not round).

_________ meters2

3. Stephanie just redecorated her bedroom. She wants to paint her door green but needs to know the surface area of the door to see if she has enough paint.



What is the surface area of the door?

_________ cm2

4. Amir is building a birdhouse that looks like a castle. The diagram shows the roof of the birdhouse. He plans to paint the roof red, but needs to know the surface area to buy the right amount of paint.



What is the surface area of the roof, including the bottom?

Give an exact answer (do not round).

_________ m2


Surface area word problems - Answers

1. It will take 24,500  cm2 of paper to make each tree.

2. It will take 21.4 m2 of material to make the tent.

3. The surface area of the door is 33,680 cm2.

4. The surface area of the roof is 0.64 m2.