In parallelogram ABCD,AB = 6,BC = 8, and $\angle A = 45^\circ.$ Find the area of the parallelogram.

Question

asked Jan 23, 2021 37.1k views

1 Answer

Jaredsk · Answer 1 · 2021-01-28T16:18:27+0000

Answer:

$\huge\boxed{A=24\sqrt2}$

Explanation:

Look at the pictures.

In the ΔAED the sides are in the proportion
$1:1:\sqrt2$

Therefore we have the equation:

$|AE|\sqrt2=6\qquad\text{multiply both sides by}\ \sqrt2\\\\2|AE|=6\sqrt2\qquad\text{divide both sides by 2}\\\\|AE|=3\sqrt2$

Therefore

$|ED|=3\sqrt2$

The formula of an area of a parallelogram:

$A=bh\\\\b-base\\h-height$

We have

$base=|AB|=8\\height=|ED|=3\sqrt2$

Substitute:

$A=(8)(3\sqrt2)=24\sqrt2$

$In parallelogram ABCD,AB = 6,BC = 8, and $\angle A = 45^\circ.$ Find the area of the-example-1$

$In parallelogram ABCD,AB = 6,BC = 8, and $\angle A = 45^\circ.$ Find the area of the-example-2$