Q13. - Geometry

Question

Find the area of each figure:

A parallelogram with${45}^{\circ }$ angle and sides 6and 10

Step-by-Step Solution

Answer

The area of given figure is$30\sqrt{2}$ square units.

Step 1. Given information.

The sides of parallelogram are 6 and 10.

Angle is ${45}^{\circ }$

Step 2. Find height of Parallelogram.

In triangle$AED$

$sin{45}^{\circ }=\frac{h}{6}$

$\frac{1}{\sqrt{2}}=\frac{h}{6}$

$$" width="9" height="19" style="max-width: none; vertical-align: -4px;" >$h=3\sqrt{2}$

Step 3. Find the area of given figure.

Since the area of parallelogram can be found using the formula

$A=bh$

$A=10\times 3\sqrt{2}$

   $=30\sqrt{2}$  Square units.

Therefore, the area of given figure is$30\sqrt{2}$ square units.