Question

the area of parallelogram wxyz is approximately 45 square units. what is the approximate perimeter of the parallelogram? o 5 units o 15 units o 30 units o 40 units trigonometric area formula area = 1/2 ab sin(c)

Explanation:

Step1: Use area formula to find side - length

Given area formula $A=\frac{1}{2}ab\sin(C)$ for a triangle formed within the parallelogram. Let one side of the parallelogram $a = 10$, and assume the other - side is $b$. The area of the parallelogram is approximately 45 square units. The area of $\triangle WZY$ (half of the parallelogram) is $A_{triangle}=\frac{45}{2}=22.5$ square units. Using the formula $A_{triangle}=\frac{1}{2}ab\sin(C)$ with $a = 10$, $C = 115^{\circ}$, and $A_{triangle}=22.5$. We have $22.5=\frac{1}{2}\times10\times b\times\sin(115^{\circ})$. Since $\sin(115^{\circ})\approx0.9063$, then $22.5 = 5\times b\times0.9063$. Solving for $b$ gives $b=\frac{22.5}{5\times0.9063}=\frac{22.5}{4.5315}\approx5$.

Step2: Calculate the perimeter of the parallelogram

The perimeter $P$ of a parallelogram with adjacent - sides $a$ and $b$ is given by $P = 2(a + b)$. Here, $a = 10$ and $b\approx5$. So $P=2(10 + 5)=30$ units.

Answer:

30 units