Question

A right prism has height 8 and triangular bases with sides of length 7, 8, and 9. What is the: Total surface area of the prism?

Answer 1

the total surface area of the prism is 245.67

Explanation:

Given;

height of the triangular prism, h = 8

length of the triangular bases, = 7, 8, and 9

The total surface area of the prism is calculated as;

T.S.A = ph + 2B

Where;

p is the perimeter of the base

B is area of the base

P = 7 + 8 + 9 = 24

Area of the base can be calculated using Hero's formula;

`S = (7+8+9)/(2) = 12\\\\Base \ area (B) = √(12(12-7)(12-8)(12-9)) = 26.833`

T.S.A = (24 x 8) + 2 x 26.833

T.S.A = 192 + 53.666

T.S.A = 245.67

Therefore, the total surface area of the prism is 245.67