Question

Find the lateral surface area of the triangular prism.​

Answer 1

Answer:

$A=108\ in^2$

Step-by-step explanation:

Lateral Surface Area

It's the sum of the five surface areas formed by the prism. There are two identical triangles (front and back surfaces) and three rectangles (bottom, lateral and upward).

Each triangle has a base of 4 in and a height of 3 in. The area of each triangle is

$\displaystyle A_t=\frac{bh}{2}=\frac{4\cdot 3}{2}=6\ in^2$

The total area of the triangles is twice that value, or $12\ in^2$

The area of the lateral rectangle is

$A_l=3\cdot 8=24\ in^2$

The area of the bottom rectangle is

$A_b=4\cdot 8=32\ in^2$

The area of the upward rectangle is

$A_u=5\cdot 8=40\ in^2$

The total lateral area is

$A=12+24+32+40=108\ in^2$