Area and volume problems worksheet

Grade 7 math, Common Core 7.G.B.6. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Area and volume problems

Grade 7 math, Common Core 7.G.B.6

Solve each problem. Include the units.

1.
An open box (no top) is 12 in long, 7 in wide and 8 in tall. How much cardboard does it take?
2.
An open box (no top) is 8 in long, 6 in wide and 8 in tall. How much cardboard does it take?
3.
A tent is a triangular prism. Its triangle end has a base of 12 ft and a height of 4 ft, and the tent is 15 ft long. What is its volume?
4.
An open box (no top) is 7 in long, 3 in wide and 5 in tall. How much cardboard does it take?
5.
A tent is a triangular prism. Its triangle end has a base of 10 ft and a height of 4 ft, and the tent is 9 ft long. What is its volume?
6.
A fish tank is 39 cm long, 25 cm wide and 24 cm tall. How many cubic centimeters of water does it hold when full?
7.
A fish tank is 32 cm long, 22 cm wide and 12 cm tall. How many cubic centimeters of water does it hold when full?
8.
An open box (no top) is 11 in long, 6 in wide and 5 in tall. How much cardboard does it take?
9.
An open box (no top) is 10 in long, 4 in wide and 2 in tall. How much cardboard does it take?
10.
An L-shaped patio is a 12 ft by 7 ft rectangle with a 6 ft by 4 ft rectangle cut out of one corner. What is its area?

Answer key: Area and volume problems

Grade 7 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. 388 in²
Bottom: 84Front and back: 2 × 96 = 192Sides: 2 × 56 = 112Total: 388
2. 272 in²
Bottom: 48Front and back: 2 × 64 = 128Sides: 2 × 48 = 96Total: 272
3. 360 ft³
Base: 12 × 12 × 4 = 2424 × 15 = 360
4. 121 in²
Bottom: 21Front and back: 2 × 35 = 70Sides: 2 × 15 = 30Total: 121
5. 180 ft³
Base: 12 × 10 × 4 = 2020 × 9 = 180
6. 23,400 cm³
39 × 25 × 24 = 23,400
7. 8,448 cm³
32 × 22 × 12 = 8,448
8. 236 in²
Bottom: 66Front and back: 2 × 55 = 110Sides: 2 × 30 = 60Total: 236
9. 96 in²
Bottom: 40Front and back: 2 × 20 = 40Sides: 2 × 8 = 16Total: 96
10. 60 ft²
12 × 7 = 846 × 4 = 2484 − 24 = 60

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About area and volume problems

Real problems often mix shapes. Split a shape into rectangles and triangles, find each area, and add (or subtract for holes and cut-out corners). The volume of any prism is the area of its base times its height, which works for rectangular and triangular prisms alike.

Worked example 1

A tent is a triangular prism. Its triangle end has a base of 14 ft and a height of 5 ft, and the tent is 13 ft long. What is its volume?

Step 1.Base: 12 × 14 × 5 = 35
Step 2.35 × 13 = 455

Answer: 455 ft³

Worked example 2

A fish tank is 36 cm long, 24 cm wide and 27 cm tall. How many cubic centimeters of water does it hold when full?

Step 1.36 × 24 × 27 = 23,328

Answer: 23,328 cm³

Worked example 3

An open box (no top) is 10 in long, 8 in wide and 7 in tall. How much cardboard does it take?

Step 1.Bottom: 80
Step 2.Front and back: 2 × 70 = 140
Step 3.Sides: 2 × 56 = 112
Step 4.Total: 332

Answer: 332 in²

Watch out for

Draw and label a quick sketch before you calculate.
For a triangular prism, the base is the triangle: 12 × b × h, then multiply by the length.
An open box has 5 faces, not 6.

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