#### Answer

30 $in^{2}$

#### Work Step by Step

Area of triangle = $\frac{1}{2} \times b \times h$
b= 12 in
h is unknown
Since the triangle is a right-angled triangle, h can be found using the Pythagorean Theorem which states that that the square of the hypotenuse is equal to the sum of the square of the other two sides
$12^{2}+h^{2}=13^{2}$
Solving algebraically:
$h^{2}=13^{2}-12^{2}$
$h^{2}=25$
$h=\sqrt 25 =5$
Thus, Area of triangle
= $\frac{1}{2} \times b \times h$
= $\frac{1}{2} \times 12 \times 5$
= 30 $in^{2}$