Question

a parallelogram, with dimensions in centimeters, is shown in the diagram below. what is the area of the parallelogram, in square centimeters? 60 80 112 142

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 \(6\) and the hypotenuse \(c = 10\). Then \(h=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8\)

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 \(10\) (the side parallel to the base we use for the formula, here assume the base length is \(10\) (the non - slant side related to the right - triangle's height calculation, actually the base for area formula can be considered as \(10\) in the context of the problem's dimension setup, or more accurately, if we consider the base as \(10\) (the side adjacent to the right - triangle part in terms of the figure's structure for area calculation using the height we found)). \(A=10\times8 = 80\)

Answer:

B. \(80\)