Lesson 3 Homework Practice Surface Area Of Rectangular Prisms

[Harold Yengo]

Lesson 3 Homework Practice Surface Area Of Rectangular Prisms

In this lesson, you will learn how to find the surface area of rectangular prisms using nets. A net is a flat shape that can be folded to make a 3D object. The surface area of a 3D object is the total area of all its faces.

To find the surface area of a rectangular prism using a net, follow these steps:

Lesson 3 Homework Practice Surface Area Of Rectangular Prisms

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• Draw a net of the rectangular prism. A net of a rectangular prism consists of six rectangles that are arranged in a specific way. You can use the dimensions of the prism to label the lengths and widths of the rectangles.

• Find the area of each rectangle in the net. To find the area of a rectangle, multiply its length by its width.

• Add up the areas of all the rectangles in the net. This is the surface area of the rectangular prism.

Here is an example of how to apply these steps:

The net of the rectangular prism has six rectangles. The areas of the rectangles are:

• Rectangle 1: 4 cm x 3 cm = 12 cm

• Rectangle 2: 4 cm x 2 cm = 8 cm

• Rectangle 3: 4 cm x 3 cm = 12 cm

• Rectangle 4: 4 cm x 2 cm = 8 cm

• Rectangle 5: 3 cm x 2 cm = 6 cm

• Rectangle 6: 3 cm x 2 cm = 6 cm

The surface area of the rectangular prism is the sum of the areas of all the rectangles:

Surface area = 12 cm + 8 cm + 12 cm + 8 cm + 6 cm + 6 cm

Surface area = 52 cm

You can check your answer by using the formula for the surface area of a rectangular prism:

Surface area = 2(lw + lh + wh)

Surface area = 2(4 x 3 + 4 x 2 + 3 x 2)

Surface area = 2(12 + 8 + 6)

Surface area = 2(26)

Surface area = 52 cm

You can also use this formula to find the surface area of a rectangular prism without drawing a net, but it is helpful to visualize how the net relates to the prism.

Practice Problems

Try these practice problems to test your understanding of finding the surface area of rectangular prisms using nets.

• A rectangular prism has dimensions of 5 m by 4 m by 3 m. Draw a net of the prism and find its surface area.

• A cereal box has dimensions of 20 cm by 10 cm by 30 cm. Draw a net of the box and find its surface area.

• A gift box has dimensions of 15 in by 12 in by 4 in. Draw a net of the box and find its surface area.

Solutions

• A rectangular prism has dimensions of 5 m by m by <

strong>m by <

strong>m by <

strong>m by <

strong>m by <

strong>m by <

strong>m by <

strong>m by <

strong>3 m. Draw a net of the prism and find its surface area.

A possible net of the prism is shown below:

The areas of the rectangles in the net are:

• Rectangle 1: 5 m x 4 m = 20 m

• Rectangle 2: 5 m x 3 m = 15 m

• Rectangle 3: 5 m x 4 m = 20 m

• Rectangle 4: 5 m x 3 m = 15 m

• Rectangle 5: 4 m x 3 m = 12 m

• Rectangle 6: 4 m x 3 m = 12 m

The surface area of the prism is the sum of the areas of all the rectangles:

Surface area = 20 m + 15 m + 20 m + 15 m + 12 m + 12 m

Surface area = 94 m

• A cereal box has dimensions of 20 cm by m by <

strong>m by <

strong>m by <

strong>m by <

strong>m by <

strong>m by <

strong>m by <

strong>m by <

strong>m by <

strong>30 cm. Draw a net of the box and find its surface area.

A possible net of the box is shown below:

The areas of the rectangles in the net are:

• Rectangle 1: 20 cm x 10 cm = 200 cm

• Rectangle 2: 20 cm x 30 cm = 600 cm

• Rectangle 3: 20 cm x 10 cm = 200 cm

• Rectangle 4: 20 cm x 30 cm = 600 cm

• Rectangle 5: 10 cm x 30 cm = 300 cm

• Rectangle 6: 10 cm x 30 cm = 300 cm

The surface area of the box is the sum of the areas of all the rectangles:

Surface area = 200 cm + 600 cm + 200 cm+600cm<^2^>+300cm<^2^>+300cm<^2^>

Surface area = 2200cm^2^

• A gift box has dimensions of 15 in by <12 in by 4 in. Draw a net of the box and find its surface area.

A possible net of the box is shown below:

The areas of the rectangles in the net are:

Rectangle 1 : 15 in x 12 in = 180 in ^ 2 ^

• Rectangle 2: 15 in x 4 in = 60 in

• Rectangle 3: 15 in x 12 in = 180 in

• Rectangle 4: 15 in x 4 in = 60 in

• Rectangle 5: 12 in x 4 in = 48 in

• Rectangle 6: 12 in x 4 in = 48 in

The surface area of the box is the sum of the areas of all the rectangles:

Surface area = 180 in + 60 in + 180 in+60in<^2^>+48in<^2^>+48in<^2^>

Surface area = 576in^2^

You have now learned how to find the surface area of rectangular prisms using nets. You can use this skill to solve real-world problems involving packaging, painting, wrapping, and more. Remember to draw a net of the prism, find the area of each rectangle, and add them up to get the surface area.

Review Questions

To check your understanding of this lesson, answer the following questions:

• What is a net of a rectangular prism?

• What is the formula for the surface area of a rectangular prism?

• What are the steps to find the surface area of a rectangular prism using a net?

• A rectangular prism has dimensions of 8 cm by 6 cm by 10 cm. Find its surface area using a net.

• A juice box has dimensions of 3 in by 2 in by 5 in. Find its surface area using a net.

Answers

• A net of a rectangular prism is a flat shape that can be folded to make the prism. It consists of six rectangles that are arranged in a specific way.

• The formula for the surface area of a rectangular prism is Surface area = 2(lw + lh + wh), where l, w, and h are the length, width, and height of the prism.

• The steps to find the surface area of a rectangular prism using a net are:

• Draw a net of the rectangular prism. Label the lengths and widths of the rectangles with the dimensions of the prism.

• Find the area of each rectangle in the net. Multiply its length by its width.

• Add up the areas of all the rectangles in the net. This is the surface area of the rectangular prism.

• A rectangular prism has dimensions of 8 cm by <6 cm by 10 cm. Find its surface area using a net.

A possible net of the prism is shown below:

The areas of the rectangles in the net are:

Rectangle 1 : 8 cm x 6 cm = 48 cm ^ 2 ^

• Rectangle 2: 8 cm x 10 cm = 80 cm

• Rectangle 3: 8 cm x 6 cm = 48 cm

• Rectangle 4: 8 cm x 10 cm = 80 cm

• Rectangle 5: 6 cm x 10 cm = 60 cm

• Rectangle 6: 6 cm x 10 cm = 60 cm

The surface area of the prism is the sum of the areas of all the rectangles:

Surface area = 48 cm + 80 cm + 48 cm+80cm<^2^>+60cm<^2^>+60cm<^2^>

Surface area = 376cm^2^

• A juice box has dimensions of 3 in by <2 in by 5 in. Find its surface area using a net.

A possible net of the box is shown below:

The areas of the rectangles in the net are:

Rectangle 1 : 3 in x 2 in = 6 in ^ 2 ^

• Rectangle 2: 3 in x 5 in = 15 in

• Rectangle 3: 3 in x 2 in = 6 in

• Rectangle 4: 3 in x 5 in = 15 in

• Rectangle 5: 2 in x 5 in = 10 in

• Rectangle 6: 2 in x 5 in = 10 in

The surface area of the box is the sum of the areas of all the rectangles:

Surface area = 6 in + 15 in + 6 in+15in<^2^>+10in<^2^>+10in<^2^>

Surface area = 62in^2^

This is the end of the article. I hope you enjoyed learning about finding the surface area of rectangular prisms using nets. You can use this knowledge to solve various problems involving geometry and measurement. If you have any questions or feedback, please let me know.

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