Surface Area of Triangular Prisms online exercise for | Live ... - Free Printable

Explanation:
We are finding the surface area of each triangular prism. A triangular prism has:

- 2 triangular bases (identical), and
- 3 rectangular lateral faces.

So, surface area =
 (area of triangle base × 2) + (area of rectangle 1 + rectangle 2 + rectangle 3)

But in these diagrams, the prism is shown “unfolded” — the shaded region is one triangular base plus three rectangles attached to its sides. However, the problem asks for the *total surface area*, which includes both triangular bases.

Let’s solve each one carefully.

---

Problem 1:
Triangle base:
- Base = 12 in
- Height = 8 in (shown with right angle)
→ Area of one triangle = (1/2) × base × height = (1/2) × 12 × 8 = 48 in²
→ Two triangles = 2 × 48 = 96 in²

Now the three rectangles:
Each rectangle has height equal to the length of the prism (the side perpendicular to the triangle), and width equal to a side of the triangle.

From diagram:
- Triangle sides: 10 in, 10 in, 12 in
- The prism length (side connecting the two triangles) is given as 14 in (label on the slanted rectangle).

So rectangles have dimensions:
- 10 in × 14 in → area = 140 in²
- 10 in × 14 in → area = 140 in²
- 12 in × 14 in → area = 168 in²

Sum of rectangles = 140 + 140 + 168 = 448 in²

Total surface area = triangles + rectangles = 96 + 448 = 544 in²

✔ Double-check: Yes — triangle sides match the rectangle widths; prism length is consistent (14 in). Correct.

---

Problem 2:
Triangle base: right triangle
- Legs: 5 ft and 12 ft
→ Area of one triangle = (1/2) × 5 × 12 = 30 ft²
→ Two triangles = 60 ft²

Triangle sides:
- Two legs: 5 ft, 12 ft
- Hypotenuse: given as 13 ft (since 5-12-13 is a Pythagorean triple, and it's labeled)

Prism length (height of rectangles) = 19 ft (label on the slanted rectangle)

Rectangles:
- 5 ft × 19 ft = 95 ft²
- 12 ft × 19 ft = 228 ft²
- 13 ft × 19 ft = 247 ft²

Sum of rectangles = 95 + 228 + 247 = 570 ft²

Total surface area = 60 + 570 = 630 ft²

✔ Check: 5² + 12² = 25 + 144 = 169 = 13² → correct hypotenuse. Good.

---

Problem 3:
Triangle base: appears to be scalene. Given:
- One side = 9 yd (base)
- Height to that base = 14 yd (dashed line with right angle)
→ Area of one triangle = (1/2) × 9 × 14 = 63 yd²
→ Two triangles = 126 yd²

Other triangle sides: labeled 18 yd and 20 yd
Prism length (height of rectangles) = 17 yd (label on slanted rectangle)

Rectangles:
- 9 yd × 17 yd = 153 yd²
- 18 yd × 17 yd = 306 yd²
- 20 yd × 17 yd = 340 yd²

Sum of rectangles = 153 + 306 + 340 = 799 yd²

Total surface area = 126 + 799 = 925 yd²

✔ Check: All sides used once; height corresponds to base 9 yd; prism length is 17 yd — matches all rectangles. Correct.

Final Answer:
1) 544 in²
2) 630 ft²
3) 925 yd²