Question

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

Explanation:

Step1: Divide the polygon into rectangles

We can divide the given polygon into two rectangles. One rectangle has dimensions 9 by $(14 + 3)$ and the other has dimensions $(27 - 9 - 7)$ by $(14+3)$ and a small rectangle with dimensions 7 by 3.

Step2: Calculate the area of the first large rectangle

The first large - rectangle has length $l_1=9$ and width $w_1 = 17$ (since $14 + 3=17$). The area $A_1=l_1\times w_1=9\times17 = 153$.

Step3: Calculate the area of the second large rectangle

The second large - rectangle has length $l_2=27-(9 + 7)=11$ and width $w_2 = 17$. The area $A_2=l_2\times w_2=11\times17 = 187$.

Step4: Calculate the area of the small rectangle

The small rectangle has length $l_3 = 7$ and width $w_3=3$. The area $A_3=l_3\times w_3=7\times3 = 21$.

Step5: Calculate the total area of the polygon

The total area $A = A_1+A_2+A_3=153 + 187+21=361$ (This is wrong. Let's try another way).

Let's divide it into three rectangles:

1. A rectangle with length 9 and height 28 ($14 + 14$). Area $A_1=9\times28 = 252$.
2. A rectangle with length $(27 - 9)$ and height 14. Area $A_2=(27 - 9)\times14=18\times14 = 252$.
3. A rectangle with length 7 and height 3. Area $A_3=7\times3 = 21$.

Step6: Calculate the total area

$A=A_1+A_2+A_3=252+252 + 21=525$.

Answer:

C. 525 square units