Question

WORTH 12 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! HELP ASAP

Answer 1

`\large\boxed{S.A.=1,000\ u^2}`

Explanation:

We have two congruent right triangles and three rectangles.

First, calculate the length of the hypotenuse using the Pythagorean theorem:

`leg^2+leg^2=hypotenuse^2`

We have

`leg=8,\ leg=15,\ hypotenuse=h`

Substitute:

`h^2=8^2+15^2\\\\h^2=64+225\\\\h^2=289\to h=√(289)\\\\h=17`

The formula of an area of a right triangle:

`A_t=((leg)(leg))/(2)`

Substitute:

`A_t=((8)(15))/(2)=(4)(15)=60`

The formula of an area of a rectangle:

`A=wl`

w - width

l - length

Rectangle 1:

w = 15, l = 22

`A_1=(15)(22)=330`

Rectangle 2:

w = 17, l = 22

`A_2=(17)(22)=374`

Rectangle 3:

w = 8, l = 22

`A_3=(8)(22)=176`

The Surface Area of the triangular prism:

`S.A.=2A_t+A_1+A_2+A_3`

Substitute:

`S.A.=2(60)+330+374+176=1,000`