# Calculate x, y, Perimeter and area of the composite geometrical figure?

May 8, 2016

We should assume that $F G$ $| |$ $C E$, $A B = A I$ and $A G = A I$.
Otherwise, the problem is not properly defined.
$x = 16$
$y = 12$
Area=$896$

#### Explanation:

From the right triangle $\Delta C D E$, using Pythagorean Theorem,
$C D = \sqrt{{20}^{2} - {12}^{2}} = 16$

From this follows that $x = A G = A B = C D = 16$

Hence,
$y = A D - 12 - x = 40 - 12 - 16 = 12$

Area:
$40 \cdot 16 + 16 \cdot 16 = 896$