Surface Area of a Triangular Prism Worksheets - Free Printable

To find the surface area of a triangular prism, we need to add up the areas of all its faces. A triangular prism has:
- 2 triangular bases (front and back)
- 3 rectangular lateral faces (sides)

The formula is:
Surface Area = 2 × (Area of Triangle) + (Perimeter of Triangle × Length of Prism)

Or simply: Add the area of the two triangles and the three rectangles.

Here are the step-by-step solutions for each problem:

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1)
* Triangles: Base = 8 in, Height = 6 in.
Area of one triangle = $\frac{1}{2} \times 8 \times 6 = 24$ sq in.
Two triangles = $24 \times 2 = 48$ sq in.
* Rectangles: The sides of the triangle are 8 in, 10 in, and 10 in. The length of the prism is 5 in.
Rectangle 1: $8 \times 5 = 40$ sq in.
Rectangle 2: $10 \times 5 = 50$ sq in.
Rectangle 3: $10 \times 5 = 50$ sq in.
Total Rectangles = $40 + 50 + 50 = 140$ sq in.
* Total Surface Area: $48 + 140 = 188$ sq in.

2)
* Triangles: Base = 9 ft, Height = 12 ft.
Area of one triangle = $\frac{1}{2} \times 9 \times 12 = 54$ sq ft.
Two triangles = $54 \times 2 = 108$ sq ft.
* Rectangles: The sides of the triangle are 9 ft, 12 ft, and 15 ft. The length of the prism is 1 ft.
Rectangle 1: $9 \times 1 = 9$ sq ft.
Rectangle 2: $12 \times 1 = 12$ sq ft.
Rectangle 3: $15 \times 1 = 15$ sq ft.
Total Rectangles = $9 + 12 + 15 = 36$ sq ft.
* Total Surface Area: $108 + 36 = 144$ sq ft.

3)
* Triangles: Base = 6 yd, Height = 4 yd.
Area of one triangle = $\frac{1}{2} \times 6 \times 4 = 12$ sq yd.
Two triangles = $12 \times 2 = 24$ sq yd.
* Rectangles: The sides of the triangle are 5 yd, 5 yd, and 6 yd. The length of the prism is 2 yd.
Rectangle 1: $5 \times 2 = 10$ sq yd.
Rectangle 2: $5 \times 2 = 10$ sq yd.
Rectangle 3: $6 \times 2 = 12$ sq yd.
Total Rectangles = $10 + 10 + 12 = 32$ sq yd.
* Total Surface Area: $24 + 32 = 56$ sq yd.

4)
* Triangles: Base = 5 ft, Height = 2 ft.
Area of one triangle = $\frac{1}{2} \times 5 \times 2 = 5$ sq ft.
Two triangles = $5 \times 2 = 10$ sq ft.
* Rectangles: The sides of the triangle are 3 ft, 4 ft, and 5 ft. The length of the prism is 11 ft.
Rectangle 1: $3 \times 11 = 33$ sq ft.
Rectangle 2: $4 \times 11 = 44$ sq ft.
Rectangle 3: $5 \times 11 = 55$ sq ft.
Total Rectangles = $33 + 44 + 55 = 132$ sq ft.
* Total Surface Area: $10 + 132 = 142$ sq ft.

5)
* Triangles: Base = 9 yd, Height = 3 yd.
Area of one triangle = $\frac{1}{2} \times 9 \times 3 = 13.5$ sq yd.
Two triangles = $13.5 \times 2 = 27$ sq yd.
* Rectangles: The sides of the triangle are 6 yd, 6 yd, and 9 yd. The length of the prism is 7 yd.
Rectangle 1: $6 \times 7 = 42$ sq yd.
Rectangle 2: $6 \times 7 = 42$ sq yd.
Rectangle 3: $9 \times 7 = 63$ sq yd.
Total Rectangles = $42 + 42 + 63 = 147$ sq yd.
* Total Surface Area: $27 + 147 = 174$ sq yd.

6)
* Triangles: Base = 12 m, Height = 16 m.
Area of one triangle = $\frac{1}{2} \times 12 \times 16 = 96$ sq m.
Two triangles = $96 \times 2 = 192$ sq m.
* Rectangles: The sides of the triangle are 16 m, 20 m, and 12 m. The length of the prism is 17 m.
Rectangle 1: $16 \times 17 = 272$ sq m.
Rectangle 2: $20 \times 17 = 340$ sq m.
Rectangle 3: $12 \times 17 = 204$ sq m.
Total Rectangles = $272 + 340 + 204 = 816$ sq m.
* Total Surface Area: $192 + 816 = 1008$ sq m.

7)
* Triangles: Base = 10 yd, Height = 12 yd.
Area of one triangle = $\frac{1}{2} \times 10 \times 12 = 60$ sq yd.
Two triangles = $60 \times 2 = 120$ sq yd.
* Rectangles: The sides of the triangle are 13 yd, 13 yd, and 10 yd. The length of the prism is 17 yd.
Rectangle 1: $13 \times 17 = 221$ sq yd.
Rectangle 2: $13 \times 17 = 221$ sq yd.
Rectangle 3: $10 \times 17 = 170$ sq yd.
Total Rectangles = $221 + 221 + 170 = 612$ sq yd.
* Total Surface Area: $120 + 612 = 732$ sq yd.

8)
* Triangles: Base = 12 in, Height = 5 in.
Area of one triangle = $\frac{1}{2} \times 12 \times 5 = 30$ sq in.
Two triangles = $30 \times 2 = 60$ sq in.
* Rectangles: The sides of the triangle are 5 in, 12 in, and 13 in. The length of the prism is 15 in.
Rectangle 1: $5 \times 15 = 75$ sq in.
Rectangle 2: $12 \times 15 = 180$ sq in.
Rectangle 3: $13 \times 15 = 195$ sq in.
Total Rectangles = $75 + 180 + 195 = 450$ sq in.
* Total Surface Area: $60 + 450 = 510$ sq in.

9)
* Triangles: Base = 13 ft, Height = 8.4 ft.
Area of one triangle = $\frac{1}{2} \times 13 \times 8.4 = 54.6$ sq ft.
Two triangles = $54.6 \times 2 = 109.2$ sq ft.
* Rectangles: The sides of the triangle are 8.5 ft, 8.5 ft, and 13 ft. The length of the prism is 10 ft.
Rectangle 1: $8.5 \times 10 = 85$ sq ft.
Rectangle 2: $8.5 \times 10 = 85$ sq ft.
Rectangle 3: $13 \times 10 = 130$ sq ft.
Total Rectangles = $85 + 85 + 130 = 300$ sq ft.
* Total Surface Area: $109.2 + 300 = 409.2$ sq ft.

Final Answer:
1) 188 sq in
2) 144 sq ft
3) 56 sq yd
4) 142 sq ft
5) 174 sq yd
6) 1008 sq m
7) 732 sq yd
8) 510 sq in
9) 409.2 sq ft