Question

what is the area of the parallelogram shown below? units² show calculator

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the parallelogram be \(h\). Using the right - triangle formed (with hypotenuse \(17\) and one leg \(8\)), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 17\) and \(a = 8\), then \(h=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}=\sqrt{25\times9}=\sqrt{225}=15\).

Step2: Calculate the area of the parallelogram

The formula for the area of a parallelogram is \(A=\text{base}\times\text{height}\). The base \(b = 9\) and height \(h = 15\), so \(A=9\times15 = 135\).

Answer:

\(135\)