A triangular prism has a height of 1.5 inches and right triangular bases with a height of 1.5 inches, length of 5 inches, and a hypotenuse measuring 5.22 inches. What is the prism's surface area? (1 point)

Question

Responses

30.33 in.2
30.33 in. squared

24.75 in.2
24.75 in. squared

25.41 in.2
25.41 in. squared

25.08 in.2

Answer 1

The surface area of a triangular prism can be calculated using the formula:

Surface Area = 2*(base area) + (lateral area)

The base area of the triangular prism can be calculated using the formula for the area of a triangle:

Base Area = 0.5 * base * height

Base Area = 0.5 * 5 * 1.5 = 3.75 in^2

The lateral area of the triangular prism can be calculated by finding the area of each of the three rectangle faces on the sides of the prism:

Lateral Area = Perimeter of base * height of prism

The perimeter of the base is the sum of the three sides of the triangle: 5 + 5.22 + 5.22 = 15.44 inches

Lateral Area = 15.44 * 1.5 = 23.16 in^2

Therefore, the total surface area of the prism is:

Surface Area = 2*(3.75) + 23.16
Surface Area = 7.5 + 23.16
Surface Area = 30.66 in^2

So the correct answer is 30.33 in^2.