Question

What is the surface area of the following triangular prism?

Answer 1

Yooo you go to aoa too?!?

Answer 2

You can solve the surface area of a triangular prism using these formulas:
$SA=2A_{B}+(a+b+c)h$

Where:
AB = Area of the triangle
a = side of triangular base
b = side of triangular base
c = side of triangular base
h = height 

Take note that there the height of the triangular face is not given. So you will need an alternate formula for the area. Since the sides are given you use Heron's formula.

$A_{B}= \sqrt{s(s-a)(s-b)(s-c)}$

S is not given, so you can solve this by adding all the sides of the triangular base and dividing it by two. 

$s = \frac{a+b+c}{2}$

a = 3yd
b = 5yd
c= 4yd

$s=\frac{a+b+c}{2}$
$s=\frac{3yd+5yd+4yd}{2}$
$s=\frac{12yd}{2}$
$s=6yd$

Now that we have s, we can insert that into the formula for the area of the triangular face:

$A_{B}= \sqrt{6yd(6yd-3yd)(6yd-5yd)(6yd-4yd)}$
$A_{B}= \sqrt{6yd(3yd)(1yd)(2yd)}$
$A_{B}= \sqrt{36yd^{4})}$
$A_{B}= 6yd^{2}$

Now that we have the area of the triangle, we can solve now for the surface area of the triangular prism:

$SA=2A_{B}+(a+b+c)h$
$SA=2(6yd^{2}+(3yd+4yd+5yd)7yd$
$SA=12yd^{2}+(21yd^{2}+28yd^{2}+35yd^{2})$
$SA=12yd^{2}+(84yd^{2})$
$SA=96yd^{2}$

The answer is then $96yd^{2}$.