Question

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

Answer 1

Answer:

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

Step-by-step 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:

$h^2=8^2+15^2\\\\h^2=64+225\\\\h^2=289\to h=\sqrt{289}\\\\h=17$

The formula of an area of a right triangle:

$A_t=\dfrac{(leg)(leg)}{2}$

Substitute:

$A_t=\dfrac{(8)(15)}{2}=(4)(15)=60$

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:

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