Question

a parallelogram, with dimensions in centimeters, is shown in the diagram below. what is the area of the parallelogram, in square centimeters? 15 44 55 72

Explanation:

Step1: Find the height of the parallelogram

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) in the right - triangle. Let the height \(h\) (one leg of the right - triangle), the other leg is \(3\) and the hypotenuse is \(5\). Then \(h=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}=4\).

Step2: Calculate the area of the parallelogram

The formula for the area of a parallelogram is \(A = base\times height\). The base of the parallelogram is \(8 + 3=11\) (by observing the length along the base - like side) and the height \(h = 4\). So \(A=11\times4 = 44\).

Answer:

44