EXPLANATION
The area of the figure can be obtained by applying the following relationship:
[tex]Area_{paralle\log ram}=base\cdot height[/tex]Where b=base and height=h
In order to find the height, we need to apply the trigonometric relationship:
[tex]\sin 45=\frac{opposite}{\text{hypotenuse}}=\frac{height}{\text{diagonal}}=\frac{h}{6.4}[/tex]Multiplying both sides by 6.4:
[tex]6.4\cdot\sin 45=h[/tex]Solving the argument:
[tex]6.4\cdot0.65=h[/tex]Switching sides:
[tex]h=4.16\text{ inches}[/tex]Now that we have the height, we can compute the area as follows:
[tex]\text{Area}_{\text{parallelogram}}=12.8in\cdot4.16in=53.24in^2[/tex]The answer is 53.24 squared inches.
