Question

What is the total area of the prism?

Answer 1

Answer:

The total area of the prism is $SA=(\frac{9\sqrt{3}}{2}+54)\ in^{2}$

Step-by-step explanation:

we know that

The surface area of the triangular prism of the figure is equal to

$SA=2B+PL$

where

B is the area of the triangular face

P is the perimeter of the triangular face

L is the length of the prism

Find the area of the base B

The base is an equilateral triangle

so

Applying the law of sines the area is equal to

$B=\frac{1}{2}(3)^{2}sin(60\°)$

$B=\frac{9\sqrt{3}}{4}\ in^{2}$

Find the perimeter P of the triangular face

$P=(3+3+3)=9\ in$

we have

$L=6\ in$

substitute

$SA=2(\frac{9\sqrt{3}}{4})+(9)(6)$

$SA=(\frac{9\sqrt{3}}{2}+54)\ in^{2}$