use formulas to find the lateral and surface area of the given prism
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.
round to the nearest whole
To find the lateral area of a prism, we need to find the perimeter of its base and multiply it by the height of the prism. The perimeter of a right triangle is the sum of its sides, so we can find the perimeter of the base as:
perimeter = 6 + 9 + 10.82 = 25.82 meters
Then, the lateral area of the prism is:
lateral area = perimeter x height = 25.82 x 26 = 671.32 square meters
To find the surface area of the prism, we need to find the area of each face and add them up. The area of the base is:
area = (1/2) x 6 x 9 = 27 square meters
Since there are two congruent triangular faces, the total area of both is:
area = 2 x (1/2) x 6 x 26 = 156 square meters
Then, the surface area of the prism is:
surface area = 2 x area of base + total area of faces = 2 x 27 + 156 = 210 square meters