Question
Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
A right triangular prism is shown. The legs of the right triangle base measure 2 meters and 5 meters. The hypotenuse measures 5.39 meters. The height of the prism is 26 meters.
(1 point)
Responses
322 m2; 327 m2
322 m 2 ; 327 m 2
296 m2; 342 m2
296 m 2 ; 342 m 2
296 m2; 332 m2
296 m 2 ; 332 m 2
322 m2; 332 m2
322 m 2 ; 332 m 2
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To find the lateral area of a prism, you would use the formula LA = ph, where L is the length of the triangle base, and h is the height of the prism.
In this case, the length of the triangle base is 5 meters, and the height of the prism is 26 meters. So, the lateral area would be LA = 5 * 26 = 130 square meters.
To find the surface area of the prism, you would use the formula SA = 2B + LA, where B is the area of the triangle base.
The area of the triangle base can be found using Heron's formula: A = sqrt(s(s - a)(s - b)(s - c)), where a, b, and c are the lengths of the triangle sides, and s is the semiperimeter (s = (a + b + c)/2).
In this case, the lengths of the triangle sides are 2, 5, and 5.39 meters. The semiperimeter is s = (2 + 5 + 5.39)/2 = 6.695 meters.
So, the area of the triangle base would be A = sqrt(6.695(6.695 - 2)(6.695 - 5)(6.695 - 5.39)) = sqrt(6.695(0.695)(1.695)(1.305)) = sqrt(6.460) ≈ 2.54 square meters.
Therefore, the surface area would be SA = 2(2.54) + 130 = 5.08 + 130 = 135.08 square meters.
Rounding to the nearest whole number, the lateral area is 130 m2, and the surface area is 135 m2.
So, the correct answer is (1) 322 m2; 327 m2.