Answer:
[tex]\large\boxed{S.A.=1,000\ u^2}[/tex]
Step-by-step explanation:
We have two congruent right triangles and three rectangles.
First, calculate the length of the hypotenuse using the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=8,\ leg=15,\ hypotenuse=h[/tex]
Substitute:
[tex]h^2=8^2+15^2\\\\h^2=64+225\\\\h^2=289\to h=\sqrt{289}\\\\h=17[/tex]
The formula of an area of a right triangle:
[tex]A_t=\dfrac{(leg)(leg)}{2}[/tex]
Substitute:
[tex]A_t=\dfrac{(8)(15)}{2}=(4)(15)=60[/tex]
The formula of an area of a rectangle:
[tex]A=wl[/tex]
w - width
l - length
Rectangle 1:
w = 15, l = 22
[tex]A_1=(15)(22)=330[/tex]
Rectangle 2:
w = 17, l = 22
[tex]A_2=(17)(22)=374[/tex]
Rectangle 3:
w = 8, l = 22
[tex]A_3=(8)(22)=176[/tex]
The Surface Area of the triangular prism:
[tex]S.A.=2A_t+A_1+A_2+A_3[/tex]
Substitute:
[tex]S.A.=2(60)+330+374+176=1,000[/tex]
