# In an isosceles trapezoid ABCD, AB=CD=5. The top base = 8 and the bottom base = 14. What is the area of this trapezoid?

Dec 26, 2015

Area: $44$

#### Explanation:

see diagram below:
$\textcolor{b l a c k}{\text{specified values in black}}$;
$\textcolor{red}{\text{calculated values in red}}$

Extracting a rectangle from the center section of the isosceles trapezoid leaves two right angled triangles with bases of $3$ and hypotenuses of $5$
which implies a trapezoid height of $4$ (since $3 : 4 : 5$ is a standard right angled triangle).

Area of trapezoid = ("base" + "top")/2 xx "height"

$\textcolor{w h i t e}{\text{XXXXXXXXX}} = \frac{14 + 8}{2} \times 4 = 44$