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 = $\frac{1}{2}absin(c)$

Explanation:

Step1: Use area formula to find side - length

The area of a parallelogram can be written as \(A = ab\sin(C)\). In parallelogram \(WXYZ\), assume \(a = 10\) and \(C=115^{\circ}\), and \(A = 45\). We know \(A=\frac{1}{2}ab\sin(C)\) for a triangle formed within the parallelogram. Since the area of the parallelogram \(A = ab\sin(C)\) (because the parallelogram can be thought of as composed of two congruent triangles). Substitute \(A = 45\), \(a = 10\), and \(C = 115^{\circ}\) (\(\sin(115^{\circ})\approx0.9063\)) into \(A=ab\sin(C)\). Then \(45=10\times b\times0.9063\). Solving for \(b\):
\[b=\frac{45}{10\times0.9063}\approx5\]

Step2: Calculate the perimeter

The perimeter \(P\) of a parallelogram with adjacent - side lengths \(a\) and \(b\) is \(P = 2(a + b)\). Here \(a = 10\) and \(b\approx5\). So \(P=2(10 + 5)=30\)

Answer:

30 units