If I have a triangular prism with the length of 9mm, the base of 6.6 mm, and the height 4 mm or 5.2 mm. What would be the surface area?

The surface area of triangular prism is 117.12 mm²

Explanation:

Base side, a = 9 mm

Base side, b = 6.6 mm

Base side, c = 5.2 mm

Height, h = 4 mm

Total surface area = ?

We know,

Surface area, A = 2 Ab (a+b+c) h

Ab = √s (s-a) (s-b) (s-c)

s = a+b+c/2

Solving for A

A = ah + b h + ch + 1/2 √ - a⁴ + 2 (ab) ² + 2 (ac) ² - b⁴ + 2 (b c) ² - c⁴

A = 9.4 + 6.6 X 4 + 5.2 X 4 + 1//2 √ - 9⁴ + 2 (9 X 6.6) ² + 2 (9 X 5.2) ² - (6.6) ⁴ + 2 (6.6 X 5.2) ² - (5.2) ⁴

A = 117.12 mm²

Therefore, the surface area of triangular prism is 117.12 mm²