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
To find the lateral area of a prism, you calculate the perimeter of the base and then multiply it by the height of the prism.
The perimeter of the triangular base is (6 + 9 + 10.82) = 25.82 meters.
Therefore, the lateral area of the prism is 25.82 * 26 = 671 m².
To find the surface area of the prism, you calculate the lateral area as well as the areas of the two triangular bases.
The area of each triangular base is (1/2) * 6 * 9 = 27 m².
So, the total surface area of the prism is 671 + 2(27) = 671 + 54 = 725 m².
Therefore, the lateral area is 671 m² and the surface area is 725 m².
Therefore, the correct answer is 671 m²; 725 m².