Let’s solve each problem one by one. We’ll find the surface area of each 3D shape using its net. The net shows all the faces laid out flat, so we just need to find the area of each face and add them up.
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Problem 1: Cube (all sides 3 yd)
A cube has 6 identical square faces.
Each face is a square with side = 3 yd
Area of one face = 3 × 3 = 9 sq yd
Total surface area = 6 × 9 =
54 sq yd
✔ Check: All edges are 3 yd → yes, it’s a cube → 6 faces → correct.
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Problem 2: Rectangular Prism (7 cm × 4 cm × 6 cm)
This prism has 3 pairs of identical rectangles:
- Front & back: 7 cm × 6 cm → area = 42 sq cm each → total for both = 84 sq cm
- Left & right: 4 cm × 6 cm → area = 24 sq cm each → total for both = 48 sq cm
- Top & bottom: 7 cm × 4 cm → area = 28 sq cm each → total for both = 56 sq cm
Add them: 84 + 48 + 56 =
84 + 48 = 132
132 + 56 =
188 sq cm
✔ Check: Net shows those dimensions — matches. Formula for rectangular prism SA = 2(lw + lh + wh) = 2(7×4 + 7×6 + 4×6) = 2(28+42+24)=2(94)=188 → correct.
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Problem 3: Triangular Prism
The net shows:
- Two triangular bases
- Three rectangular sides
First, triangles: base = 6 m, height = 8 m (from diagram — perpendicular height inside triangle)
Area of one triangle = (base × height)/2 = (6 × 8)/2 = 48/2 = 24 sq m
Two triangles = 2 × 24 = 48 sq m
Now rectangles:
- One rectangle: 10 m × 13 m? Wait — let’s look carefully.
Actually, from the net:
- The three rectangles have heights equal to the length of the prism (which is 13 m), and widths equal to the sides of the triangle: 6 m, 8 m, and 10 m.
Wait — in the triangle, sides are 6 m, 8 m, and 10 m? Let’s check if it’s a right triangle: 6² + 8² = 36 + 64 = 100 = 10² → YES! So it’s a right triangle with legs 6 and 8, hypotenuse 10.
So the three rectangular faces are:
- 6 m × 13 m = 78 sq m
- 8 m × 13 m = 104 sq m
- 10 m × 13 m = 130 sq m
Sum of rectangles = 78 + 104 + 130
78 + 104 = 182
182 + 130 = 312 sq m
Add triangles: 312 + 48 =
360 sq m
✔ Check: Total surface area = lateral area + 2×base area = (perimeter of base × height) + 2×(area of base)
Perimeter = 6+8+10=24 m; height of prism = 13 m → lateral area = 24×13=312
Base area = 24 → 2×24=48 → total 360 → correct.
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Problem 4: Square Pyramid
Net shows:
- One square base: 10 in × 10 in
- Four triangular faces: each has base 10 in and slant height 9 in (given on diagram)
Area of square base = 10 × 10 = 100 sq in
Area of one triangle = (base × height)/2 = (10 × 9)/2 = 90/2 = 45 sq in
Four triangles = 4 × 45 = 180 sq in
Total surface area = 100 + 180 =
280 sq in
✔ Check: Base is square, 4 identical triangles — yes. Slant height given as 9 in — used correctly. No trick here.
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Final Answer:
1. 54 sq yd
2. 188 sq cm
3. 360 sq m
4. 280 sq in
Parent Tip: Review the logic above to help your child master the concept of nets worksheet.
