Question

so, I need to just find the missing length, if you can, please explain the pythagorean theorem to find the missing side. I don't understand, please hurry. also the answer is 828 I just need to explain how I got that answer, thanks.

Answer 1

The surface area of the triangular prism is 828 in².

Solution:

Let the missing length of the triangle be x.

Using Pythagoras theorem,

In right triangle, square of the hypotenuse is equal to the sum of the squares of other two sides.

$12^2+x^2=15^2$

$144+x^2=225$

Subtract 144 on both sides of the equation.

$x^2=225-144$

$x^2=81$

Taking square root on both sides, we get

x = 9

The missing length of the triangle is 9 in.

Area of the front triangle = $\frac{1}{2}\times 12\times 9$

                                         = 54 in²

Area of the back triangle = $\frac{1}{2}\times 12\times 9$

                                         = 54 in²

Area of the sloping rectangle = 20 × 9

                                                 = 180 in²

Area of the back rectangle = 20 × 12

                                             = 240 in²

Area of the base rectangle = 20 × 15

                                             = 300 in²

Total area = 54 in² + 54 in² + 180 in² + 240 in² + 300 in²

                 = 828 in²

The surface area of the triangular prism is 828 in².