Question

find the area of the parallelogram below by using the area formulas for rectangles and triangles.
a = 12 cm, b = 15 cm, and c = 6 cm
*picture not drawn to scale
a. 180 cm²
b. 189 cm²
c. 144 cm²
d. 90 cm²

Explanation:

Step1: Divide the parallelogram

Divide the parallelogram into a rectangle and a right - triangle.

Step2: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A_{rectangle}=a\times b\). Given \(a = 12\mathrm{cm}\) and \(b = 15\mathrm{cm}\), but we need to correct the base for the rectangle - like part. The height of the parallelogram (which is the same as the side \(a = 12\mathrm{cm}\)) and the base of the non - triangle part: assume the base of the rectangle part is \(b_1=b - c\). Since \(b = 15\mathrm{cm}\) and \(c=6\mathrm{cm}\), then \(b_1 = 15 - 6=9\mathrm{cm}\). The area of the rectangle \(A_{rectangle}=12\times9 = 108\mathrm{cm}^2\)

Step3: Calculate the area of the triangle

The formula for the area of a triangle is \(A_{triangle}=\frac{1}{2}\times c\times a\). Substitute \(c = 6\mathrm{cm}\) and \(a = 12\mathrm{cm}\) into the formula: \(A_{triangle}=\frac{1}{2}\times6\times12=36\mathrm{cm}^2\)

Step4: Calculate the area of the parallelogram

The area of the parallelogram \(A = A_{rectangle}+A_{triangle}\). So \(A=108 + 36=144\mathrm{cm}^2\)

Answer:

C. \(144\mathrm{cm}^2\)