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?

Question

A: 25.08 in.2

B: 24.75 in.2

C: 25.41 in.2

D: 30.33 in.2

Answer 1

The area of each of the triangular bases is $$\frac{1}{2}(\text{base})(\text{height})=\frac{1}{2}(5)(1.5)=3.75.$$The three lateral faces each have an area of $$\frac{1}{2}(\text{base})(\text{height})=\frac{1}{2}(5.22)(1.5)=3.915.$$Therefore, the total surface area is $$3\cdot 3.915+2\cdot 3.75=\boxed{\textbf{(A) }25.08 \text{ in.}^2}.$$

Answer 2

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?

A: 25.08 inches squared.

B: 24.75 inches squared.

C: 25.41 inches squared.

D: 30.33 inches squared.

Answer 3

The area of each of the triangular bases is $$\frac{1}{2}(\text{base})(\text{height})=\frac{1}{2}(5)(1.5)=3.75.$$The three lateral faces each have an area of $$\frac{1}{2}(\text{base})(\text{height})=\frac{1}{2}(5.22)(1.5)=3.915.$$Therefore, the total surface area is $$3\cdot 3.915+2\cdot 3.75=\boxed{\textbf{(A) }25.08 \text{ in.}^2}.$$

Answer 4

i cant read that. can you write just in english?

Answer 5

Sure! Here's a simplified version of the solution:

The triangular prism has two triangular bases and three rectangular lateral faces. The area of each base is 3.75 square inches, and the area of each lateral face is 3.915 square inches. To find the total surface area, we can add up the areas of all five faces. This gives us:

Total surface area = (area of base) x 2 + (area of lateral face) x 3
Total surface area = 3.75 x 2 + 3.915 x 3
Total surface area = 25.08 square inches

Therefore, the surface area of the triangular prism is 25.08 square inches, which is answer choice (A).