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
To find the lateral area of a right triangular prism, use the formula: Lateral Area = perimeter of base x height
First, calculate the perimeter of the base triangle:
Perimeter = 6 + 9 + 10.82 = 25.82 meters
Now, calculate the lateral area:
Lateral Area = 25.82 x 26 = 671.32 m2
To find the surface area of the prism, you need to add the area of the two triangular bases.
First, calculate the area of one triangular base:
Area = 1/2 x base x height
Area = 1/2 x 6 x 9 = 27 m2
Now, calculate the total surface area:
Surface Area = 2(27) + 671.32
Surface Area = 54 + 671.32 = 725.32 m2
Rounded to the nearest whole number, the lateral area is 671 m2 and the surface area is 725 m2.
So the correct response is:
671 m2; 725 m2