The surface area of a right triangular prism is 228 square inches. The base is a right triangle with a height of 6 inches and a base length of 8 inches. The length of the third side of the base is 10 inches. Find the height of the prism.
Answer (3)
l oo k a t t h e p i c t u re A re a = 228 i n 2 A re a = 2 A 1 + A 2 + A 3 + A 4 2 A 1 = 2 ⋅ 2 6 ⋅ 8 = 48 ( i n 2 ) A 2 = 8 H A 3 = 6 H A 4 = 10 H
48 + 8 H + 6 H + 10 H = 228 48 + 24 H = 228 / − 48 24 H = 180 / : 24 H = 7.5 ( in )
The height of right triangular prism is 7.5 in. ;
The height of the right triangular prism is 7.5 inches. This was calculated using the area of the base triangle and the total surface area formula of the prism. By setting up the equation and solving for the height, we found the value to be 7.5 inches.
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