Question

A isosceles triangular prism has a height of `15 cm`, the perimeter of the base is `32 cm` and the base of the triangle is `6/5` the side. Calculate the surface area of the prism?

Answer 1

Surface area of prism `color(maroon)(A_T = 576 cm^2`

Explanation:

Total Surface Area of prism = 2 * base Area + lateral surface area of the prism

Given `h = 15cm, p = 32cm, b = c, a = (6/5)b`

`a + b + c = p`

`(6/5)b + b + b = 32`

`16b = 32*5, b = 10cm`

`a = (6/5)b = (6/5)*10 = 12cm`

Semi perimeter `s = (a + b + c)/2 = (12+10+10)/2 = 16cm`

Area of base triangle `A_t = sqrt( s (s-a) (s-b) (s-c))`

`A_t = sqrt(16*(16-12)(16-10)(16-10)) = 48 cm^2`

Lateral Surface Area of prism `A_l = 2 * b * h + a * h`

`A_l = 2 * 10 * 15 + 12*15 = 480 cm^2`

`color(maroon)(T S A = A_T = 2 * A_t + A_l = 2 * 48 + 480 = 576 cm^2`