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
a. 189 cm²
b. 144 cm²
c. 180 cm²
d. 90 cm²

Explanation:

Step1: Find the base of the rectangle

The base of the rectangle is \(b - c=15 - 6=9\mathrm{cm}\)

Step2: Calculate the area of the rectangle

The area of the rectangle is \(A_{1}=a\times(b - c)=12\times9 = 108\mathrm{cm}^{2}\)

Step3: Calculate the area of the two triangles

The two triangles can be combined into a single rectangle with base \(c = 6\mathrm{cm}\) and height \(a = 12\mathrm{cm}\). The area of the two - triangle combination is \(A_{2}=a\times c=12\times6=72\mathrm{cm}^{2}\)

Step4: Calculate the area of the parallelogram

The area of the parallelogram \(A=A_{1}+A_{2}=108 + 72=180\mathrm{cm}^{2}\)

Answer:

C. \(180\mathrm{cm}^{2}\)