MATH SOLVE

2 months ago

Q:
# 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.

Accepted Solution

A:

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

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