## Thinking Mathematically (6th Edition)

30 $in^{2}$
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 $in^{2}$