Question

how much Square cm is the area of the polygon?

Answer 1

Notice that we can divide the polygon in two regular polygons:

then, we can find the area separately:

$\begin{gathered} Area\text{ of the square:} \\ A_1=12\cdot12=144\operatorname{cm}^2 \\ \text{Area of the triangle:} \\ A_2=\frac{12\cdot19}{2}=\frac{228}{2}=114\operatorname{cm}^2 \end{gathered}$

adding both areas, we get:

$A=A_1+A_2=144\operatorname{cm}+114\operatorname{cm}=258\operatorname{cm}^2$

therefore, the area of the polygon is 258 square centimeters