# In a right- angled triangle, the base of a right angled triangle is 12 cm and its hypotenuse is 13 cm. How do you find the area of the triangle?

Mar 16, 2018

The area is 30 cm squared

#### Explanation:

Let's put $12$ in as $a$ and $13$ in as $c$ (13 is the hypotenuse, so it must go in the position of c, and 12 is one of the legs since it is not the hypotenuse). In order to find the area, we need to do base times height divided by two, so we need to find the height of the triangle (the other leg).

${12}^{2} + {b}^{2} = {13}^{2}$

$144 + {b}^{2} = 169$

${b}^{2} = 25$

$b = \pm 5 \rightarrow$ Disregard the negative answer because a side length cannot be negative

The height is 5 cm.

Find the area:

$\frac{12 \cdot 5}{2}$

$\frac{60}{2}$

$30 \rightarrow$ The area is 30 cm squared