Question

What is the surface area of the net of the triangular prism? (1 point) H=8 L=6 A=10 B=10 C=10

Answer 1

The formula for finding the surface area of a triangular prism is SA = 2(A) + Ph, where A is the area of the triangular base, P is the perimeter of the base, and h is the height of the prism.

The area of the base triangle (A) can be found using Heron's formula:
s = (a + b + c) / 2 = (10 + 10 + 6) / 2 = 13
A = √(s(s-a)(s-b)(s-c))
A = √(13(13-10)(13-10)(13-6))
A = √(13(3)(3)(7))
A = √(819)
A ≈ 28.64

The perimeter of the base (P) is the sum of the lengths of the three sides:
P = a + b + c = 10 + 10 + 6 = 26

The height of the prism (h) is given as 8.

Plugging these values into the formula SA = 2(A) + Ph:
SA = 2(28.64) + 26(8)
SA ≈ 57.28 + 208
SA ≈ 265.28

Therefore, the surface area of the net of the triangular prism is approximately 265.28 square units.