← Back to the Surface Area And Volume Of Prisms worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 7.G.B.6 · Level: Grade 7
Problem 1 Area with a notch
Whole rectangle: 13 × 10 = 130 m². Notch: 5 × 4 = 20 m².
130 − 20 = 110.
110 m²
Problem 2 House outline
Rectangle: 12 × 7 = 84 m². Triangle: ½ × 12 × 5 = 30 m².
84 + 30 = 114.
114 m²
Problem 3 Volume of a box
V = lwh = 11 × 3 × 8 = 264.
264 in³
Problem 4 Surface area of a box
SA = 2(lw + lh + wh) = 2(21 + 35 + 15) = 2(71) = 142.
142 ft²
Problem 5 Triangular prism volume
B = ½ × 9 × 4 = 18 cm². V = Bh = 18 × 15 = 270.
270 cm³
Problem 6 Cube measurements
V = 7³ = 343. Each face is 7 × 7 = 49, and there are 6 faces: SA = 6 × 49 = 294.
V = 343 cm³; SA = 294 cm²
Problem 7 Trapezoid area
A = ½(11 + 17) × 6 = ½ × 28 × 6 = 84.
84 m²
Problem 8 Volume from base area
V = Bh = 36.5 × 12 = 438.
438 cm³
Problem 9 Missing height
Base area: 12 × 5 = 60 in². h = V ÷ B = 360 ÷ 60 = 6.
6 in
Problem 10 Triangular prism surface area
Base area: B = ½ × 8 × 15 = 60 in². Perimeter: 8 + 15 + 17 = 40 in.
SA = 2B + Ph = 2(60) + 40 × 9 = 120 + 360 = 480.
480 in²
Problem 11 T-shaped figure
Top: 18 × 5 = 90 m². Stem: 6 × 9 = 54 m².
90 + 54 = 144.
144 m²
Problem 12 Stacked blocks
Bottom: 12 × 8 × 3 = 288 cm³. Top: 6 × 8 × 4 = 192 cm³.
288 + 192 = 480.
480 cm³
Problem 13 Missing base of a triangle
A = ½bh, so 84 = ½ × b × 12 = 6b. Then b = 84 ÷ 6 = 14.
14 cm
Problem 14 Air in a tent
B = ½ × 6 × 4 = 12 ft². V = 12 × 8 = 96.
96 ft³
Problem 15 Swimming pool
Treat the trapezoid as the base: B = ½(3 + 8) × 20 = 110 ft². V = 110 × 10 = 1,100 ft³.
Gallons: 1,100 × 7.5 = 8,250.
1,100 ft³, about 8,250 gallons
Problem 16 Painting a crate
SA = 2(5 × 3 + 5 × 2.5 + 3 × 2.5) = 2(15 + 12.5 + 7.5) = 2(35) = 70 ft².
70 ÷ 40 = 1.75, so 2 whole quarts are needed.
70 ft²; 2 quarts
Problem 17 Carpet cost
Area: 20 × 12 + 8 × 6 = 240 + 48 = 288 ft².
Cost: 288 × 2.75 = 792.
$792.00
Problem 18 Chocolate box
B = ½ × 10 × 12 = 60 cm². V = 60 × 20 = 1,200.
Perimeter: 10 + 13 + 13 = 36 cm. SA = 2(60) + 36 × 20 = 120 + 720 = 840.
V = 1,200 cm³; SA = 840 cm²
Problem 19 Concrete steps
The side view is made of columns 3 ft wide with heights 2, 3 and 5 ft: area = 3(2) + 3(3) + 3(5) = 30 ft².
V = 30 × 4 = 120.
120 ft³
Problem 20 Slab with a block
Slab: 2(100) + 4(10 × 4) = 200 + 160 = 360 cm². Cube: 6 × 36 = 216 cm².
The glued region is 6 × 6 = 36 cm², hidden on both solids: 360 + 216 − 2(36) = 504.
504 cm²