Question

two sides of a parallelogram are 450 feet and 650 feet. the measure of the angle between these sides is 62°. find the area of the parallelogram to the nearest square foot.

Explanation:

Step1: Recall area formula for parallelogram

The area $A$ of a parallelogram with sides $a$, $b$ and included angle $\theta$ is $A = a \cdot b \cdot \sin(\theta)$.

Step2: Substitute given values

Here, $a=450$, $b=650$, $\theta=62^\circ$.
$A = 450 \times 650 \times \sin(62^\circ)$

Step3: Calculate the value

First compute $\sin(62^\circ) \approx 0.88295$.
Then $450 \times 650 = 292500$.
$A \approx 292500 \times 0.88295 \approx 258262.875$

Step4: Round to nearest square foot

Round $258262.875$ to the nearest whole number.

Answer:

258263 square feet