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 6 meters and 9 meters. The hypotenuse measures 10.82 meters. The height of the prism is 26 meters.
(1 point)
Responses
645 m2; 779 m2
645 m 2 ; 779 m 2
671 m2; 725 m2
671 m 2 ; 725 m 2
645 m2; 725 m2
645 m 2 ; 725 m 2
671 m2; 698 m2
671 m 2 ; 698 m 2
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To find the lateral area of a prism, you need to find the perimeter of the base and multiply it by the height of the prism.
The perimeter of the base of a right triangle can be found by adding the lengths of all three sides. In this case, the legs of the right triangle base measure 6 meters and 9 meters, and the hypotenuse measures 10.82 meters. The perimeter is 6 + 9 + 10.82 = 25.82 meters.
Therefore, the lateral area of the prism is 25.82 meters * 26 meters = 671.32 square meters.
To find the surface area of the prism, you need to find the sum of the lateral area and the areas of the two triangular bases. The area of a triangle can be found using the formula: 1/2 * base * height.
The base and height of the right triangle base are given as 6 meters and 9 meters. Therefore, the area of each triangular base is 1/2 * 6 meters * 9 meters = 27 square meters.
Therefore, the surface area of the prism is 671.32 square meters + 2 * 27 square meters = 725.32 square meters.
Rounding to the nearest whole number, the lateral area is 671 m² and the surface area is 725 m².
Therefore, the answer is:
671 m²; 725 m²