Find the surface area of each triangular prism using the given dimensions.
Worksheet titled "Surface Area of Triangular Prisms" with nine problems, each showing a triangular prism with labeled dimensions and asking for the surface area calculation.
JPG
574×700
42.7 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #669628
⭐
Show Answer Key & Explanations
Step-by-step solution for: Solved Surface Area of Triangular Prisms Sheet 1 Find the | Chegg.com
▼
Show Answer Key & Explanations
Step-by-step solution for: Solved Surface Area of Triangular Prisms Sheet 1 Find the | Chegg.com
Let’s solve each problem one by one. We’ll find the surface area of each triangular prism.
Remember:
A triangular prism has 5 faces:
- 2 identical triangles (the bases)
- 3 rectangles (the sides)
So, Surface Area = (Area of triangle × 2) + (Area of rectangle 1 + Area of rectangle 2 + Area of rectangle 3)
We’ll use this formula for every problem.
---
Problem 1)
Triangle base: 12 in, height: 8 in → Area = (1/2)×12×8 = 48 in²
Two triangles: 48 × 2 = 96 in²
Rectangles:
- One is 10 in × 14 in = 140 in²
- One is 10 in × 14 in = 140 in² (since both slanted sides are 10 in)
- Bottom rectangle: 12 in × 14 in = 168 in²
Wait — actually, looking at the diagram: The two side rectangles are both 10 in by 14 in? But the bottom is 12 in by 14 in.
Actually, let me double-check: In a triangular prism, the three rectangles correspond to the three sides of the triangle multiplied by the length of the prism (which is 14 in here).
The triangle has sides: 10 in, 10 in, and 12 in. So yes:
Rectangle areas:
- 10 × 14 = 140
- 10 × 14 = 140
- 12 × 14 = 168
Total rectangle area = 140 + 140 + 168 = 448 in²
Total surface area = 96 + 448 = 544 in²
✔ Check: 48×2=96; 140+140=280; 280+168=448; 96+448=544 ✔️
---
Problem 2)
Triangle: base 5 ft, height 12 ft → Area = (1/2)×5×12 = 30 ft²
Two triangles: 30 × 2 = 60 ft²
Sides of triangle: 5 ft, 12 ft, 13 ft (it’s a right triangle!)
Prism length = 13 ft? Wait — look at diagram: the “length” of the prism (the distance between the two triangles) is labeled as 13 ft on the side.
Actually, in the diagram, the rectangular faces are:
- 5 ft × 13 ft
- 12 ft × 13 ft
- 13 ft × 13 ft? No — wait, the hypotenuse is 13 ft, so the third rectangle is 13 ft (hypotenuse) × 13 ft (prism length)? That doesn’t make sense.
Wait — re-examining: The prism’s “depth” or “length” is the dimension going into the page. In diagram 2, it says “13 ft” along the side edge — that’s the length of the prism.
So the three rectangles are:
- Base rectangle: 5 ft × 13 ft = 65 ft²
- Height rectangle: 12 ft × 13 ft = 156 ft²
- Hypotenuse rectangle: 13 ft × 13 ft = 169 ft²
But wait — that would mean the prism length is 13 ft, and the triangle sides are 5, 12, 13.
Yes.
So rectangle areas: 65 + 156 + 169 = 390 ft²
Triangles: 30 × 2 = 60 ft²
Total SA = 60 + 390 = 450 ft²
✔ Check: 5×13=65, 12×13=156, 13×13=169 → 65+156=221, 221+169=390; 390+60=450 ✔️
---
Problem 3)
Triangle: base 9 yd, height 15 yd → Area = (1/2)×9×15 = 67.5 yd²
Two triangles: 67.5 × 2 = 135 yd²
Sides of triangle: 9 yd, 15 yd, 18 yd? Diagram shows 18 yd as the slant side.
Prism length = 20 yd (labeled on the side)
So rectangles:
- 9 × 20 = 180
- 15 × 20 = 300
- 18 × 20 = 360
Sum = 180 + 300 + 360 = 840 yd²
Total SA = 135 + 840 = 975 yd²
✔ Check: 67.5×2=135; 180+300=480; 480+360=840; 135+840=975 ✔️
---
Problem 4)
Triangle: base 12 yd, height 16 yd → Area = (1/2)×12×16 = 96 yd²
Two triangles: 96 × 2 = 192 yd²
Sides: 12 yd, 16 yd, 20 yd (right triangle again)
Prism length = 20 yd? Wait — diagram says “20 yd” on the side edge — that’s the prism length.
Rectangles:
- 12 × 20 = 240
- 16 × 20 = 320
- 20 × 20 = 400
Sum = 240 + 320 + 400 = 960 yd²
Total SA = 192 + 960 = 1152 yd²
✔ Check: 96×2=192; 240+320=560; 560+400=960; 192+960=1152 ✔️
---
Problem 5)
Triangle: base 12 in, height 7 in → Area = (1/2)×12×7 = 42 in²
Two triangles: 42 × 2 = 84 in²
Sides: 7 in, 12 in, 13 in? Diagram shows 13 in as the slant side — yes, 5-12-13 scaled? Wait, 7-12-13? Let’s check: 7² + 12² = 49 + 144 = 193 ≠ 169. Not right triangle.
But diagram labels the sides as 7 in (height), 12 in (base), and 13 in (slant). So we take them as given.
Prism length = 19 in (labeled on the side)
Rectangles:
- 7 × 19 = 133
- 12 × 19 = 228
- 13 × 19 = 247
Sum = 133 + 228 + 247 = 608 in²
Total SA = 84 + 608 = 692 in²
✔ Check: 42×2=84; 133+228=361; 361+247=608; 84+608=692 ✔️
---
Problem 6)
Triangle: base 8 ft, height 3 ft → Area = (1/2)×8×3 = 12 ft²
Two triangles: 12 × 2 = 24 ft²
Sides: 3 ft, 8 ft, 5 ft? Diagram shows two sides as 5 ft — so it’s an isosceles triangle with base 8 ft, height 3 ft, and equal sides 5 ft.
Check: half-base is 4, height 3 → hypotenuse = √(4²+3²)=√25=5 ✔️
Prism length = 14 ft
Rectangles:
- 5 × 14 = 70
- 5 × 14 = 70
- 8 × 14 = 112
Sum = 70 + 70 + 112 = 252 ft²
Total SA = 24 + 252 = 276 ft²
✔ Check: 12×2=24; 70+70=140; 140+112=252; 24+252=276 ✔️
---
Problem 7)
Triangle: base 6 ft, height 2 ft → Area = (1/2)×6×2 = 6 ft²
Two triangles: 6 × 2 = 12 ft²
Sides: 2 ft, 6 ft, 4 ft? Diagram shows two sides as 4 ft — so isosceles triangle with base 6 ft, height 2 ft, equal sides 4 ft.
Check: half-base 3, height 2 → hypotenuse = √(9+4)=√13 ≈ 3.6, but diagram says 4 ft — so we go with given values.
Prism length = 10 ft
Rectangles:
- 4 × 10 = 40
- 4 × 10 = 40
- 6 × 10 = 60
Sum = 40 + 40 + 60 = 140 ft²
Total SA = 12 + 140 = 152 ft²
✔ Check: 6×2=12; 40+40=80; 80+60=140; 12+140=152 ✔️
---
Problem 8)
Triangle: base 16 yd, height 15 yd → Area = (1/2)×16×15 = 120 yd²
Two triangles: 120 × 2 = 240 yd²
Sides: 15 yd, 16 yd, 17 yd? Diagram shows 17 yd as slant side — check: 8-15-17 triangle? Half-base is 8, height 15 → hypotenuse = √(64+225)=√289=17 ✔️
Prism length = 20 yd
Rectangles:
- 15 × 20 = 300
- 16 × 20 = 320
- 17 × 20 = 340
Sum = 300 + 320 + 340 = 960 yd²
Total SA = 240 + 960 = 1200 yd²
✔ Check: 120×2=240; 300+320=620; 620+340=960; 240+960=1200 ✔️
---
Problem 9)
This one is different — it’s a right triangular prism, but the right angle is at the corner of the rectangle? Wait — diagram shows a triangle with legs 6 in and 8 in, hypotenuse 10 in — classic 6-8-10 right triangle.
Area of triangle = (1/2)×6×8 = 24 in²
Two triangles: 24 × 2 = 48 in²
Prism length = 12 in (labeled on the side)
Rectangles:
- 6 × 12 = 72
- 8 × 12 = 96
- 10 × 12 = 120
Sum = 72 + 96 + 120 = 288 in²
Total SA = 48 + 288 = 336 in²
✔ Check: 24×2=48; 72+96=168; 168+120=288; 48+288=336 ✔️
---
Final Answer:
1) 544 in²
2) 450 ft²
3) 975 yd²
4) 1152 yd²
5) 692 in²
6) 276 ft²
7) 152 ft²
8) 1200 yd²
9) 336 in²
Remember:
A triangular prism has 5 faces:
- 2 identical triangles (the bases)
- 3 rectangles (the sides)
So, Surface Area = (Area of triangle × 2) + (Area of rectangle 1 + Area of rectangle 2 + Area of rectangle 3)
We’ll use this formula for every problem.
---
Problem 1)
Triangle base: 12 in, height: 8 in → Area = (1/2)×12×8 = 48 in²
Two triangles: 48 × 2 = 96 in²
Rectangles:
- One is 10 in × 14 in = 140 in²
- One is 10 in × 14 in = 140 in² (since both slanted sides are 10 in)
- Bottom rectangle: 12 in × 14 in = 168 in²
Wait — actually, looking at the diagram: The two side rectangles are both 10 in by 14 in? But the bottom is 12 in by 14 in.
Actually, let me double-check: In a triangular prism, the three rectangles correspond to the three sides of the triangle multiplied by the length of the prism (which is 14 in here).
The triangle has sides: 10 in, 10 in, and 12 in. So yes:
Rectangle areas:
- 10 × 14 = 140
- 10 × 14 = 140
- 12 × 14 = 168
Total rectangle area = 140 + 140 + 168 = 448 in²
Total surface area = 96 + 448 = 544 in²
✔ Check: 48×2=96; 140+140=280; 280+168=448; 96+448=544 ✔️
---
Problem 2)
Triangle: base 5 ft, height 12 ft → Area = (1/2)×5×12 = 30 ft²
Two triangles: 30 × 2 = 60 ft²
Sides of triangle: 5 ft, 12 ft, 13 ft (it’s a right triangle!)
Prism length = 13 ft? Wait — look at diagram: the “length” of the prism (the distance between the two triangles) is labeled as 13 ft on the side.
Actually, in the diagram, the rectangular faces are:
- 5 ft × 13 ft
- 12 ft × 13 ft
- 13 ft × 13 ft? No — wait, the hypotenuse is 13 ft, so the third rectangle is 13 ft (hypotenuse) × 13 ft (prism length)? That doesn’t make sense.
Wait — re-examining: The prism’s “depth” or “length” is the dimension going into the page. In diagram 2, it says “13 ft” along the side edge — that’s the length of the prism.
So the three rectangles are:
- Base rectangle: 5 ft × 13 ft = 65 ft²
- Height rectangle: 12 ft × 13 ft = 156 ft²
- Hypotenuse rectangle: 13 ft × 13 ft = 169 ft²
But wait — that would mean the prism length is 13 ft, and the triangle sides are 5, 12, 13.
Yes.
So rectangle areas: 65 + 156 + 169 = 390 ft²
Triangles: 30 × 2 = 60 ft²
Total SA = 60 + 390 = 450 ft²
✔ Check: 5×13=65, 12×13=156, 13×13=169 → 65+156=221, 221+169=390; 390+60=450 ✔️
---
Problem 3)
Triangle: base 9 yd, height 15 yd → Area = (1/2)×9×15 = 67.5 yd²
Two triangles: 67.5 × 2 = 135 yd²
Sides of triangle: 9 yd, 15 yd, 18 yd? Diagram shows 18 yd as the slant side.
Prism length = 20 yd (labeled on the side)
So rectangles:
- 9 × 20 = 180
- 15 × 20 = 300
- 18 × 20 = 360
Sum = 180 + 300 + 360 = 840 yd²
Total SA = 135 + 840 = 975 yd²
✔ Check: 67.5×2=135; 180+300=480; 480+360=840; 135+840=975 ✔️
---
Problem 4)
Triangle: base 12 yd, height 16 yd → Area = (1/2)×12×16 = 96 yd²
Two triangles: 96 × 2 = 192 yd²
Sides: 12 yd, 16 yd, 20 yd (right triangle again)
Prism length = 20 yd? Wait — diagram says “20 yd” on the side edge — that’s the prism length.
Rectangles:
- 12 × 20 = 240
- 16 × 20 = 320
- 20 × 20 = 400
Sum = 240 + 320 + 400 = 960 yd²
Total SA = 192 + 960 = 1152 yd²
✔ Check: 96×2=192; 240+320=560; 560+400=960; 192+960=1152 ✔️
---
Problem 5)
Triangle: base 12 in, height 7 in → Area = (1/2)×12×7 = 42 in²
Two triangles: 42 × 2 = 84 in²
Sides: 7 in, 12 in, 13 in? Diagram shows 13 in as the slant side — yes, 5-12-13 scaled? Wait, 7-12-13? Let’s check: 7² + 12² = 49 + 144 = 193 ≠ 169. Not right triangle.
But diagram labels the sides as 7 in (height), 12 in (base), and 13 in (slant). So we take them as given.
Prism length = 19 in (labeled on the side)
Rectangles:
- 7 × 19 = 133
- 12 × 19 = 228
- 13 × 19 = 247
Sum = 133 + 228 + 247 = 608 in²
Total SA = 84 + 608 = 692 in²
✔ Check: 42×2=84; 133+228=361; 361+247=608; 84+608=692 ✔️
---
Problem 6)
Triangle: base 8 ft, height 3 ft → Area = (1/2)×8×3 = 12 ft²
Two triangles: 12 × 2 = 24 ft²
Sides: 3 ft, 8 ft, 5 ft? Diagram shows two sides as 5 ft — so it’s an isosceles triangle with base 8 ft, height 3 ft, and equal sides 5 ft.
Check: half-base is 4, height 3 → hypotenuse = √(4²+3²)=√25=5 ✔️
Prism length = 14 ft
Rectangles:
- 5 × 14 = 70
- 5 × 14 = 70
- 8 × 14 = 112
Sum = 70 + 70 + 112 = 252 ft²
Total SA = 24 + 252 = 276 ft²
✔ Check: 12×2=24; 70+70=140; 140+112=252; 24+252=276 ✔️
---
Problem 7)
Triangle: base 6 ft, height 2 ft → Area = (1/2)×6×2 = 6 ft²
Two triangles: 6 × 2 = 12 ft²
Sides: 2 ft, 6 ft, 4 ft? Diagram shows two sides as 4 ft — so isosceles triangle with base 6 ft, height 2 ft, equal sides 4 ft.
Check: half-base 3, height 2 → hypotenuse = √(9+4)=√13 ≈ 3.6, but diagram says 4 ft — so we go with given values.
Prism length = 10 ft
Rectangles:
- 4 × 10 = 40
- 4 × 10 = 40
- 6 × 10 = 60
Sum = 40 + 40 + 60 = 140 ft²
Total SA = 12 + 140 = 152 ft²
✔ Check: 6×2=12; 40+40=80; 80+60=140; 12+140=152 ✔️
---
Problem 8)
Triangle: base 16 yd, height 15 yd → Area = (1/2)×16×15 = 120 yd²
Two triangles: 120 × 2 = 240 yd²
Sides: 15 yd, 16 yd, 17 yd? Diagram shows 17 yd as slant side — check: 8-15-17 triangle? Half-base is 8, height 15 → hypotenuse = √(64+225)=√289=17 ✔️
Prism length = 20 yd
Rectangles:
- 15 × 20 = 300
- 16 × 20 = 320
- 17 × 20 = 340
Sum = 300 + 320 + 340 = 960 yd²
Total SA = 240 + 960 = 1200 yd²
✔ Check: 120×2=240; 300+320=620; 620+340=960; 240+960=1200 ✔️
---
Problem 9)
This one is different — it’s a right triangular prism, but the right angle is at the corner of the rectangle? Wait — diagram shows a triangle with legs 6 in and 8 in, hypotenuse 10 in — classic 6-8-10 right triangle.
Area of triangle = (1/2)×6×8 = 24 in²
Two triangles: 24 × 2 = 48 in²
Prism length = 12 in (labeled on the side)
Rectangles:
- 6 × 12 = 72
- 8 × 12 = 96
- 10 × 12 = 120
Sum = 72 + 96 + 120 = 288 in²
Total SA = 48 + 288 = 336 in²
✔ Check: 24×2=48; 72+96=168; 168+120=288; 48+288=336 ✔️
---
Final Answer:
1) 544 in²
2) 450 ft²
3) 975 yd²
4) 1152 yd²
5) 692 in²
6) 276 ft²
7) 152 ft²
8) 1200 yd²
9) 336 in²
Parent Tip: Review the logic above to help your child master the concept of surface area of triangular prism worksheet with answers.
![Find Surface Area Of Triangular Prism Worksheets [PDF] (7.G.B.6 ...](/images2/surface-area-of-triangular-prism-worksheet-with-answers/surface-area-of-triangular-prism-worksheet-with-answers-30.png)
