Question

question
two sides of a parallelogram are 8.6 feet and 2.2 feet. the measure of the angle between these sides is 112°. find the area of the parallelogram to the nearest 10th of a square foot.
answer
attempt 1 out of 2
ft²
submit answer
watch video
show examples

Explanation:

Step1: Recall area formula for parallelogram

The area formula for a parallelogram with adjacent - sides \(a\) and \(b\) and included - angle \(\theta\) is \(A = ab\sin\theta\).

Step2: Identify the values of \(a\), \(b\), and \(\theta\)

Here, \(a = 8.6\) feet, \(b = 2.2\) feet, and \(\theta=112^{\circ}\).

Step3: Calculate the sine of the angle

\(\sin(112^{\circ})\approx0.9272\).

Step4: Calculate the area

\(A=(8.6)\times(2.2)\times\sin(112^{\circ})\).
\(A = 8.6\times2.2\times0.9272\).
\(A = 18.92\times0.9272\).
\(A\approx17.5\) square feet.

Answer:

\(17.5\)