Question

The base of a triangular prism is an isosceles right triangle with a hypotenuse of 32−−√ centimeters. The height of the prism is 6 centimeters. Find the surface area of the triangular prism. Round your answer to the nearest tenth.

Answer 1

Isosceles triangle: two equal sides.
 We have the following relationship:
 root (32) = root (L ^ 2 + L ^ 2)
 root (32) = root (2L ^ 2)
 root (32) = Lraiz (2)
 root (32) / root (2) = L
 The surface area is:
 Area of the base and top:
 A1 = (1/2) * (root (32) / root (2)) * (root (32) / root (2))
 A1 = (1/2) * (32/2)
 A1 = (1/2) * (16)
 A1 = 8
 Area of the rectangles of equal sides:
 A2 = (root (32) / root (2)) * (6)
 A2 = 24
 Rectangle area of different side:
 A3 = (root (32)) * (6)
 A3 = 33.9411255
 The area is:
 A = 2 * A1 + 2 * A2 + A3
 A = 2 * (8) + 2 * (24) + (33.9411255)
 A = 97.9411255
 Round to the nearest tenth:
 A = 97.9 cm
 Answer:
 The surface area of the triangular prism is:
 A = 97.9 cm