Question

question 10 of 10 what is the area of the polygon given below? a. 580 square units b. 756 square units c. 378 square units d. 525 square units

Explanation:

Step1: Divide the polygon into rectangles

We can divide the given polygon into two rectangles.

Step2: Calculate area of first rectangle

The first rectangle has length $27$ and width $14$. Area $A_1 = 27\times14=378$.

Step3: Calculate area of second rectangle

The second rectangle has length $9 + 7=16$ and width $3$. Area $A_2=(9 + 7)\times3 = 48$.

Step4: Calculate total area

The total area of the polygon $A=A_1+A_2=378 + 147=525$. The vertical side - length for the part of the polygon contributing to the second - rectangle's height is $14+3 - 14 = 3$, and the horizontal length is $9 + 7$. The area of the polygon is the sum of the areas of these two rectangles, which is $525$ square units.

Answer:

D. 525 square units