Use Nets to Solve Triangular Problems Quick Check
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Question
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)
Responses
25.08 in.2
25.08 in. squared
25.41 in.2
25.41 in. squared
24.75 in.2
24.75 in. squared
30.33 in.2
To find the surface area of a triangular prism, you need to calculate the areas of each face separately.
1. The area of the two triangular bases can be calculated using the formula A = 0.5 * b * h, where b is the base and h is the height. So, for one triangular base:
A = 0.5 * 5 * 1.5 = 3.75 in^2
Since there are two bases, the total surface area for the bases is:
2 * 3.75 = 7.5 in^2
2. To find the lateral surface area, you need to find the perimeter of the base and multiply it by the height of the prism. The perimeter (P) of the base can be calculated using the Pythagorean theorem because it's a right triangle.
a^2 + b^2 = c^2
5^2 + 1.5^2 = c^2
25 + 2.25 = c^2
27.25 = c^2
c ≈ √27.25 ≈ 5.22
Therefore, the perimeter P = 5 + 5 + 5.22 ≈ 15.22
The lateral surface area is:
15.22 * 1.5 ≈ 22.83 in^2
3. Add the areas of the two bases and the lateral surface area to find the total surface area:
Total surface area = 7.5 + 22.83 ≈ 30.33 in^2
Therefore, the correct answer is: 30.33 in^2.