← Back to the Surface Area And Nets worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Each solution lists the faces, gives the area of every face and adds them. Check that the number of areas matches the number of faces, because a missing face is the most common error.
Standards: 6.G.A.4 · Level: Grade 6
Problem 1 Name the solid
The six faces are identical squares, so the net folds into a cube.
A cube with 6 faces
Problem 2 Surface area of a cube
One face is 7 × 7 = 49. The cube has 6 faces: 6 × 49 = 294.
294 square inches
Problem 3 Faces of a box net
Top and bottom: 6 × 4 = 24 each. Front and back: 6 × 2 = 12 each. Sides: 4 × 2 = 8 each. SA = 2(24) + 2(12) + 2(8) = 48 + 24 + 16 = 88.
88 square feet
Problem 4 Surface area of a box
9 × 3 = 27, 9 × 2 = 18, 3 × 2 = 6. SA = 2(27 + 18 + 6) = 2 × 51 = 102.
102 square centimeters
Problem 5 Parts of a triangular prism
Two faces are triangles and three faces are rectangles, so there are 5 faces. Count the edges: 3 on each triangle plus 3 joining them is 9 edges. There are 3 vertices on each triangle, so 6 vertices. Check: 6 − 9 + 5 = 2.
2 triangles and 3 rectangles; 5 faces, 9 edges, 6 vertices
Problem 6 Triangular prism from a net
Triangles: 12 × 9 × 12 = 54 each, so 108 for both. Rectangles: 9 × 14 = 126, 12 × 14 = 168, 15 × 14 = 210, which total 504. SA = 108 + 504 = 612.
612 square inches
Problem 7 Pyramid with a decimal slant height
Base: 6 × 6 = 36. Each triangle: 12 × 6 × 8.5 = 25.5. Four triangles: 4 × 25.5 = 102. Total: 36 + 102 = 138.
138 square meters
Problem 8 Cube with a decimal edge
One face is 3.5 × 3.5 = 12.25. Six faces: 6 × 12.25 = 73.5.
73.5 square meters
Problem 9 Missing height from surface area
220 = 2(10 × 4) + 2(10h) + 2(4h) = 80 + 28h. Then 28h = 140, so h = 5. Check: 2(40 + 50 + 20) = 220.
5 inches
Problem 10 Open-top terrarium
Bottom: 15 × 9 = 135. Two long sides: 2 × (15 × 10) = 300. Two short sides: 2 × (9 × 10) = 180. Total: 135 + 300 + 180 = 615.
615 square inches
Problem 11 Carton from a net
2(9 × 6) = 108, 2(9 × 4) = 72, 2(6 × 4) = 48. SA = 108 + 72 + 48 = 228.
228 square inches
Problem 12 Camping tent
Floor: 6 × 9 = 54. Slanted sides: 2 × (5 × 9) = 90. Triangular ends: 2 × (12 × 6 × 4) = 2 × 12 = 24. Total: 54 + 90 + 24 = 168.
168 square feet
Problem 13 Square pyramid from a net
Base: 12 × 12 = 144. Each triangle: 12 × 12 × 10 = 60, so four triangles give 240. Total: 144 + 240 = 384.
384 square inches
Problem 14 Which box needs more paper?
Box A: 2(60) + 2(40) + 2(24) = 120 + 80 + 48 = 248. Box B: 2(64) + 2(32) + 2(32) = 128 + 64 + 64 = 256. The difference is 256 − 248 = 8.
Box B has the greater surface area, by 8 square inches
Problem 15 Wrapping a gift
- 2(14 × 10) + 2(14 × 6) + 2(10 × 6) = 280 + 168 + 120 = 568.
- 568 ÷ 400 = 1.42, so 2 sheets are needed.
- 2 × 2.75 = 5.50.
(a) 568 square inches; (b) 2 sheets; (c) $5.50
Problem 16 Painting a shed
- Walls: 2(12 × 7) + 2(8 × 7) = 168 + 112 = 280. Roof: 12 × 8 = 96. Total: 376.
- 376 ÷ 100 = 3.76, so 4 gallons.
- 4 × 27.50 = 110.
(a) 376 square feet; (b) 4 gallons; (c) $110
Problem 17 Candy box
Triangles: 2 × (12 × 8 × 15) = 2 × 60 = 120. Rectangles share the length 20: (8 + 15 + 17) × 20 = 40 × 20 = 800. Total: 120 + 800 = 920.
920 square centimeters
Problem 18 Gazebo roof
Each triangle: 12 × 10 × 8 = 40. Four triangles: 4 × 40 = 160. Cost: 160 × 2.40 = 384.
$384
Problem 19 Painting a planter
- One face is 6.25 square feet. Five faces: 5 × 6.25 = 31.25 for the outside, and 31.25 for the inside. Total: 62.5.
- 62.5 ÷ 25 = 2.5, so 3 pints.
(a) 62.5 square feet; (b) 3 pints
Problem 20 Same volume, different surface
Cube: 6 × 4 × 4 = 96. Box: 2(8 × 4) + 2(8 × 2) + 2(4 × 2) = 64 + 32 + 16 = 112. The difference is 112 − 96 = 16.
Cube 96 square inches; box 112 square inches; the box is greater by 16 square inches