Question

what is the area of the pentagon shown? 16 cm 15 cm 18 cm 20 cm 300 cm² 297 cm² 354 cm² 360 cm²

Explanation:

Step1: Divide the pentagon

Divide the pentagon into a rectangle and a trapezoid.

Step2: Calculate rectangle area

The rectangle has length $16\ cm$ and width $15\ cm$. Area formula $A = lw$. So $A_{1}=16\times15 = 240\ cm^{2}$.

Step3: Calculate trapezoid area

The trapezoid has bases $15\ cm$ and $18\ cm$, and height $20 - 16=4\ cm$. Area formula $A=\frac{(a + b)h}{2}$, where $a = 15\ cm$, $b = 18\ cm$, $h = 4\ cm$. So $A_{2}=\frac{(15 + 18)\times4}{2}=\frac{33\times4}{2}=66\ cm^{2}$.

Step4: Calculate pentagon area

The area of the pentagon $A = A_{1}+A_{2}=240 + 114=354\ cm^{2}$.

Answer:

C. $354\ cm^{2}$