Question

Find the lateral area of the prism below. Round your answer to the nearest whole number.

A triangular prism has sides at each end that are right triangles. The hypotenuse is 5.39m and the sides are 2m and 5m. The prism has a length of 26m.
(1 point)
Responses

327 m2
327 m 2

296 m2
296 m 2

332 m2
332 m 2

322 m2
322 m 2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the lateral area of the triangular prism, we first need to find the area of one of the triangles at the end.

Let's use the Pythagorean Theorem to find the height of the triangle:
a^2 + b^2 = c^2
2^2 + b^2 = 5^2
4 + b^2 = 25
b^2 = 21
b = √21
b ≈ 4.58

Now, the area of one triangle is:
(1/2) * base * height
(1/2) * 2 * 4.58
≈ 4.58 m2

Since there are two triangles at the end, the total lateral area is:
2 * 4.58 * 26
≈ 238.48 m2

Rounded to the nearest whole number, the lateral area of the prism is 238 m2.

Therefore, the closest option is 236 m2.