Geometry Worksheets

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Rectangular Prism

By Dana Valdez

Learn about what rectangular prisms are and how to use them to solve problems. Find the definition, example problems, and practice problems at Thinkster Math.

Why is this concept useful?

Rectangular prisms are 3-Dimensional figures composed of six faces that are all rectangles. We use rectangular prisms in the real-world in many different situations. The volume of a rectangular prism is used to find out how much material can fit inside of it. The surface area of a rectangular prism is used to find out how much material is needed to cover it.

Where does this concept fit into the curriculum?

Grade 6

How can we use the concept:

You can find the volume and the surface area of rectangular prisms.

There are two formulas that can be used to find the volume of a rectangular prism.


V = lwh (Volume = length width height)

V = Bh (Volume = Base Area height)


The formula to find the surface area of a rectangular prism is:


A = 2(lw + lh + wh)


When finding the surface area, you are finding the area of each of the 6 rectangular faces on the prism. You can use a net, which is a 2 dimensional model of the prism. This is an example of a rectangular prism and its net:


Sample Math Problems

1. Find the surface area of the net.

Solution:

First, identify the length, width, and height:

L = 9 in W = 4 in H = 3 in


Next substitute the dimensions into the formula:

A = 2(lw + lh + wh)A = 2(9×4+9×3 +4×3)A=150 in2 \begin{array}{l} A\ =\ 2( lw\ +\ lh\ +\ wh)\\ A\ =\ 2( 9\times 4+9\times 3\ +4\times 3)\\ A=150\ in^{2} \end{array}

2. Find the surface area of a rectangular prism measuring 16 ft x 9 ft x 3.5 ft.

Solution: First, identify the length, width, and height: L = 16 ft W = 9 ft H = 3.5
Next substitute the dimensions into the formula:

A = 2(lw + lh + wh)A = 2(16×9+16×3.5 +9×3.5)A=463 in2 \begin{array}{l} A\ =\ 2( lw\ +\ lh\ +\ wh)\\ A\ =\ 2( 16\times 9+16\times 3.5\ +9\times 3.5)\\ A=463\ in^{2} \end{array}


3. Find the volume of a rectangular prism measuring 5.25 in x 9 in x 15.5 in.

Solution:

Use the formula:

V=lwhV = 5.25 × 9 × 15.5V=732.375 in3 \begin{array}{l} V=lwh\\ V\ =\ 5.25\ \times \ 9\ \times \ 15.5\\ V=732.375\ in^{3} \end{array}


4. Daniel wants to wrap a gift box in wrapping paper. The box is shaped like a rectangular prism. The base of the box is 12 inches long and 8 inches wide. The height of the box is 10 inches. What is the least amount of wrapping paper, in square inches, that Daniel will need to wrap the gift?

Solution: The dimensions of the rectangular prism are: L = 12 in, W = 8 in, H = 10 in.

A = 2(lw + lh + wh)A = 2(12×8+12×10 +8×10)A=592 in2 \begin{array}{l} A\ =\ 2( lw\ +\ lh\ +\ wh)\\ A\ =\ 2( 12\times 8+12\times 10\ +8\times 10)\\ A=592\ in^{2} \end{array}

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Practice Math Problems

1. Find the surface area of the net, in square inches, if each small square measures one square inch.

2. Find the surface area of a rectangular prism measuring 14 m x 8 m x 1.5 m.

3. Find the volume of a rectangular prism measuring 7 in x 6.35 in x 12.5 in.

4. Marie is covering a rectangular prism shaped box with blue cloth to make a decoration for her desk. The box is 5 inches long, 6 inches wide, and has a height of 7 inches. What is the fewest square inches of blue cloth Marie needs to cover the box?

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