### Home > GC > Chapter 5 > Lesson 5.3.5 > Problem5-122

5-122.

Find the area and perimeter of $ΔABC$ at right. Give approximate (decimal) answers, not exact answers.

Separate $ΔABC$ into two separate triangles by dropping the height from vertex $B$.
Label the new point $D$, creating $ΔABD$ and $ΔDBC$.

Both of the triangles that have been created are special right triangles, because the height $BD$ creates two right triangles: a $45º\text{-}45º\text{-}90º$ triangle and a $30º\text{-}60º\text{-}90º$ triangle.

The length of the hypotenuse in a $45º\text{-}45º\text{-}90º$ triangle is the length of a leg times $\sqrt{2}$.
In a $30º\text{-}60º\text{-}90º$ triangle, the length of the side opposite the $30^\circ$ angle is half of the length of the hypotenuse and the length of the side opposite the $60^\circ$ angle is half of the length of the hypotenuse times $\sqrt{3}$.