Question

What is the surface area and volume of the triangular prism?The triangular prism is 1 foot high. The triangle that forms the base of the prism has a base of 6 inches and a height of 4 inches. The two remaining sides of the triangular bases are each 5 inches long. What is the surface area and volume of the triangular prism?

Answer 1

The surface area of the triangular prism is approximately 16.222 square feet, and the volume of the triangular prism is 12 cubic feet.

Explanation:

formulas:

Surface Area = 2B + Ph

Volume = Bh

where B is the area of the triangular base, P is the perimeter of the base, h is the height of the prism, and B and h are both in the same units (inches, feet, etc.).

Given:

Height of the triangular prism = 1 foot

Base of the triangular prism = 6 inches

Height of the triangular base = 4 inches

Length of the other two sides of the triangular base = 5 inches

First, we need to find the area of the triangular base (B):

B = (1/2) x base x height

B = (1/2) x 6 inches x 4 inches

B = 12 square inches

Next, we need to find the perimeter of the triangular base (P):

P = sum of all three sides

P = 6 inches + 5 inches + 5 inches

P = 16 inches

Now, we can use the formulas to find the surface area and volume:

Surface Area = 2B + Ph

Surface Area = 2(12 square inches) + (16 inches)(1 foot)

Surface Area = 24 square inches + 16 square feet

Surface Area = 16.222 square feet (rounded to three decimal places)

Volume = Bh

Volume = 12 square inches x 1 foot

Volume = 12 cubic feet

Therefore, the surface area of the triangular prism is approximately 16.222 square feet, and the volume of the triangular prism is 12 cubic feet.