Question

In parallelogram ABCD,AB = 6,BC = 8, and ula1" title="$\angle A = 45^\circ.$" alt="$\angle A = 45^\circ.$" align="absmiddle" class="latex-formula"> Find the area of the parallelogram.

Answer 1

Answer:

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

Step-by-step 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:

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