Triangular Prism Area Worksheets - Free Printable
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Step-by-step solution for: Triangular Prism Area Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Triangular Prism Area Worksheets
Let’s solve each problem one by one. We’re calculating the surface area of triangular prisms.
A triangular prism has:
- 2 identical triangular bases
- 3 rectangular sides
So, surface area = (area of triangle × 2) + (sum of areas of the 3 rectangles)
We’ll use:
- Area of triangle = (base × height) ÷ 2
- Area of rectangle = length × width
---
Problem 1:
Triangle base = 8 m, height = 10 m → area = (8×10)/2 = 40 m²
Two triangles: 40 × 2 = 80 m²
Rectangles:
- One is 8 m × ? Wait — look at the diagram: the three rectangles have widths equal to the sides of the triangle: 8 m, 7 m, and 12.5 m? Wait — actually, in a triangular prism, the rectangles connect corresponding sides of the two triangles. The “length” of the prism (the distance between the two triangles) is given as 7 m? Wait — let me recheck.
Actually, looking at Problem 1:
The triangle has sides: 8 m (base), 10 m (height, perpendicular), and hypotenuse 12.5 m? But wait — 8-10-12.5 doesn’t satisfy Pythagoras: 8²+10²=64+100=164, √164≈12.8, not 12.5. Hmm — maybe it's labeled differently.
Wait — perhaps the 12.5 m is the slant side, and the 7 m is the length of the prism (distance between the two triangular faces).
In standard notation for these diagrams:
- The triangle has base 8 m, height 10 m → area = 40 m²
- The prism extends 7 m deep (that’s the length of the rectangles)
- The three rectangular faces are:
- Bottom: 8 m × 7 m = 56 m²
- Side: 10 m × 7 m = 70 m²? Wait — no, the 10 m is the height of the triangle, but that’s not necessarily a side of the rectangle unless it’s a right triangle with legs 8 and 10.
Actually, if the triangle is right-angled with legs 8 and 10, then hypotenuse = √(8²+10²)=√164≈12.8, but diagram says 12.5 — close enough? Maybe rounded.
But let’s assume the triangle sides are 8 m, 10 m, and 12.5 m — even if not exact right triangle, we’ll go with labels.
Then the three rectangles have dimensions:
- 8 m × 7 m = 56
- 10 m × 7 m = 70
- 12.5 m × 7 m = 87.5
Sum of rectangles: 56 + 70 + 87.5 = 213.5
Triangles: 2 × (8×10/2) = 80
Total SA = 80 + 213.5 = 293.5 m²
Wait — but is the 10 m really a side? In the diagram, the 10 m is drawn as the height inside the triangle, perpendicular to base 8 m. So yes, area of triangle is (8×10)/2 = 40.
And the three rectangles correspond to the three sides of the triangle times the depth (7 m).
Sides of triangle: base 8 m, height leg 10 m, hypotenuse 12.5 m (given).
So rectangles: 8×7, 10×7, 12.5×7 → 56, 70, 87.5 → sum 213.5
Triangles: 2×40=80
Total: 293.5 m²
But let’s check if 12.5 is correct: 8² + 10² = 164, sqrt(164)=12.806... so 12.5 is approximate. But since diagram gives 12.5, we use it.
✔ Problem 1 Answer: 293.5 m²
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Problem 2:
Triangle: base 8 m, height 7 m → area = (8×7)/2 = 28 m²
Two triangles: 56 m²
Prism length (depth) = 13 m
Triangle sides: base 8 m, height leg 7 m, hypotenuse 8.6 m (given)
Rectangles:
- 8 × 13 = 104
- 7 × 13 = 91
- 8.6 × 13 = 111.8
Sum rectangles: 104 + 91 = 195; 195 + 111.8 = 306.8
Total SA = 56 + 306.8 = 362.8 m²
Check: 8.6×13: 8×13=104, 0.6×13=7.8 → 111.8 ✔️
✔ Problem 2 Answer: 362.8 m²
---
Problem 3:
Triangle: base 13 m, height 12 m → area = (13×12)/2 = 78 m²
Two triangles: 156 m²
Prism length = 11 m
Triangle sides: base 13 m, height leg 12 m, hypotenuse 17.5 m (given)
Rectangles:
- 13 × 11 = 143
- 12 × 11 = 132
- 17.5 × 11 = 192.5
Sum rectangles: 143 + 132 = 275; 275 + 192.5 = 467.5
Total SA = 156 + 467.5 = 623.5 m²
Check: 17.5×11 = 17.5×10 + 17.5×1 = 175 + 17.5 = 192.5 ✔️
✔ Problem 3 Answer: 623.5 m²
---
Problem 4:
Triangle: base 12 m, height 13 m → area = (12×13)/2 = 78 m²
Two triangles: 156 m²
Prism length = 16 m
Triangle sides: base 12 m, height leg 13 m, hypotenuse 17.8 m (given)
Rectangles:
- 12 × 16 = 192
- 13 × 16 = 208
- 17.8 × 16 = ?
Calculate 17.8 × 16:
17 × 16 = 272
0.8 × 16 = 12.8
Total = 284.8
Sum rectangles: 192 + 208 = 400; 400 + 284.8 = 684.8
Total SA = 156 + 684.8 = 840.8 m²
✔ Problem 4 Answer: 840.8 m²
---
Problem 5:
Triangle: base 13 m, height 11 m → area = (13×11)/2 = 71.5 m²
Two triangles: 143 m²
Prism length = 14 m
Triangle sides: base 13 m, height leg 11 m, hypotenuse 14.8 m (given)
Rectangles:
- 13 × 14 = 182
- 11 × 14 = 154
- 14.8 × 14 = ?
14.8 × 14:
14 × 14 = 196
0.8 × 14 = 11.2
Total = 207.2
Sum rectangles: 182 + 154 = 336; 336 + 207.2 = 543.2
Total SA = 143 + 543.2 = 686.2 m²
✔ Problem 5 Answer: 686.2 m²
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Problem 6:
Triangle: base 12 m, height 11 m → area = (12×11)/2 = 66 m²
Two triangles: 132 m²
Prism length = 7 m
Triangle sides: base 12 m, height leg 11 m, hypotenuse 14.8 m (given)
Rectangles:
- 12 × 7 = 84
- 11 × 7 = 77
- 14.8 × 7 = ?
14.8 × 7:
14 × 7 = 98
0.8 × 7 = 5.6
Total = 103.6
Sum rectangles: 84 + 77 = 161; 161 + 103.6 = 264.6
Total SA = 132 + 264.6 = 396.6 m²
✔ Problem 6 Answer: 396.6 m²
---
Final Answers:
1. 293.5 m²
2. 362.8 m²
3. 623.5 m²
4. 840.8 m²
5. 686.2 m²
6. 396.6 m²
A triangular prism has:
- 2 identical triangular bases
- 3 rectangular sides
So, surface area = (area of triangle × 2) + (sum of areas of the 3 rectangles)
We’ll use:
- Area of triangle = (base × height) ÷ 2
- Area of rectangle = length × width
---
Problem 1:
Triangle base = 8 m, height = 10 m → area = (8×10)/2 = 40 m²
Two triangles: 40 × 2 = 80 m²
Rectangles:
- One is 8 m × ? Wait — look at the diagram: the three rectangles have widths equal to the sides of the triangle: 8 m, 7 m, and 12.5 m? Wait — actually, in a triangular prism, the rectangles connect corresponding sides of the two triangles. The “length” of the prism (the distance between the two triangles) is given as 7 m? Wait — let me recheck.
Actually, looking at Problem 1:
The triangle has sides: 8 m (base), 10 m (height, perpendicular), and hypotenuse 12.5 m? But wait — 8-10-12.5 doesn’t satisfy Pythagoras: 8²+10²=64+100=164, √164≈12.8, not 12.5. Hmm — maybe it's labeled differently.
Wait — perhaps the 12.5 m is the slant side, and the 7 m is the length of the prism (distance between the two triangular faces).
In standard notation for these diagrams:
- The triangle has base 8 m, height 10 m → area = 40 m²
- The prism extends 7 m deep (that’s the length of the rectangles)
- The three rectangular faces are:
- Bottom: 8 m × 7 m = 56 m²
- Side: 10 m × 7 m = 70 m²? Wait — no, the 10 m is the height of the triangle, but that’s not necessarily a side of the rectangle unless it’s a right triangle with legs 8 and 10.
Actually, if the triangle is right-angled with legs 8 and 10, then hypotenuse = √(8²+10²)=√164≈12.8, but diagram says 12.5 — close enough? Maybe rounded.
But let’s assume the triangle sides are 8 m, 10 m, and 12.5 m — even if not exact right triangle, we’ll go with labels.
Then the three rectangles have dimensions:
- 8 m × 7 m = 56
- 10 m × 7 m = 70
- 12.5 m × 7 m = 87.5
Sum of rectangles: 56 + 70 + 87.5 = 213.5
Triangles: 2 × (8×10/2) = 80
Total SA = 80 + 213.5 = 293.5 m²
Wait — but is the 10 m really a side? In the diagram, the 10 m is drawn as the height inside the triangle, perpendicular to base 8 m. So yes, area of triangle is (8×10)/2 = 40.
And the three rectangles correspond to the three sides of the triangle times the depth (7 m).
Sides of triangle: base 8 m, height leg 10 m, hypotenuse 12.5 m (given).
So rectangles: 8×7, 10×7, 12.5×7 → 56, 70, 87.5 → sum 213.5
Triangles: 2×40=80
Total: 293.5 m²
But let’s check if 12.5 is correct: 8² + 10² = 164, sqrt(164)=12.806... so 12.5 is approximate. But since diagram gives 12.5, we use it.
✔ Problem 1 Answer: 293.5 m²
---
Problem 2:
Triangle: base 8 m, height 7 m → area = (8×7)/2 = 28 m²
Two triangles: 56 m²
Prism length (depth) = 13 m
Triangle sides: base 8 m, height leg 7 m, hypotenuse 8.6 m (given)
Rectangles:
- 8 × 13 = 104
- 7 × 13 = 91
- 8.6 × 13 = 111.8
Sum rectangles: 104 + 91 = 195; 195 + 111.8 = 306.8
Total SA = 56 + 306.8 = 362.8 m²
Check: 8.6×13: 8×13=104, 0.6×13=7.8 → 111.8 ✔️
✔ Problem 2 Answer: 362.8 m²
---
Problem 3:
Triangle: base 13 m, height 12 m → area = (13×12)/2 = 78 m²
Two triangles: 156 m²
Prism length = 11 m
Triangle sides: base 13 m, height leg 12 m, hypotenuse 17.5 m (given)
Rectangles:
- 13 × 11 = 143
- 12 × 11 = 132
- 17.5 × 11 = 192.5
Sum rectangles: 143 + 132 = 275; 275 + 192.5 = 467.5
Total SA = 156 + 467.5 = 623.5 m²
Check: 17.5×11 = 17.5×10 + 17.5×1 = 175 + 17.5 = 192.5 ✔️
✔ Problem 3 Answer: 623.5 m²
---
Problem 4:
Triangle: base 12 m, height 13 m → area = (12×13)/2 = 78 m²
Two triangles: 156 m²
Prism length = 16 m
Triangle sides: base 12 m, height leg 13 m, hypotenuse 17.8 m (given)
Rectangles:
- 12 × 16 = 192
- 13 × 16 = 208
- 17.8 × 16 = ?
Calculate 17.8 × 16:
17 × 16 = 272
0.8 × 16 = 12.8
Total = 284.8
Sum rectangles: 192 + 208 = 400; 400 + 284.8 = 684.8
Total SA = 156 + 684.8 = 840.8 m²
✔ Problem 4 Answer: 840.8 m²
---
Problem 5:
Triangle: base 13 m, height 11 m → area = (13×11)/2 = 71.5 m²
Two triangles: 143 m²
Prism length = 14 m
Triangle sides: base 13 m, height leg 11 m, hypotenuse 14.8 m (given)
Rectangles:
- 13 × 14 = 182
- 11 × 14 = 154
- 14.8 × 14 = ?
14.8 × 14:
14 × 14 = 196
0.8 × 14 = 11.2
Total = 207.2
Sum rectangles: 182 + 154 = 336; 336 + 207.2 = 543.2
Total SA = 143 + 543.2 = 686.2 m²
✔ Problem 5 Answer: 686.2 m²
---
Problem 6:
Triangle: base 12 m, height 11 m → area = (12×11)/2 = 66 m²
Two triangles: 132 m²
Prism length = 7 m
Triangle sides: base 12 m, height leg 11 m, hypotenuse 14.8 m (given)
Rectangles:
- 12 × 7 = 84
- 11 × 7 = 77
- 14.8 × 7 = ?
14.8 × 7:
14 × 7 = 98
0.8 × 7 = 5.6
Total = 103.6
Sum rectangles: 84 + 77 = 161; 161 + 103.6 = 264.6
Total SA = 132 + 264.6 = 396.6 m²
✔ Problem 6 Answer: 396.6 m²
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Final Answers:
1. 293.5 m²
2. 362.8 m²
3. 623.5 m²
4. 840.8 m²
5. 686.2 m²
6. 396.6 m²
Parent Tip: Review the logic above to help your child master the concept of surface area of a triangular prism worksheet.
