The area of this polygon is equal to 220 cm².
Area of Compound Shapes
This exercise requires your knowledge about the area of compound shapes. For solving this, you should:
- Identify the basic shapes;
- Calculate your individual areas;
- Sum each area found.
For finding the area, the steps are presented below.
STEP 1 - Identify the basic shapes.
The polygon is composed of one triangle and one rectangle. Therefore, you should sum the area of these geometric figures.
STEP 2 - Find the area of the triangle.
Area of the triangle - [tex]A_{triangle}=\frac{bh}{2}[/tex] . The figure shows:
b= length of the base= 18-7=11 cm
h=height=15-11=4cm
Then, [tex]A_{triangle}=\frac{bh}{2}=\frac{11*4}{2}=\frac{44}{2} =22 cm^2[/tex].
STEP 3 - Find the area of the rectangle.
Area of the rectangle- [tex]A_{rectangle}=bh[/tex] . The figure shows:
b= length of the base= 18 cm
h=height= 11 cm
Then, [tex]A_{rectangle}=bh=18*11=198cm^2[/tex] .
STEP 4 - Find the area of the polygon .
[tex]A_{polygon}=A_{triangle}+A_{rectangle}\\ \\ A_{polygon}=22+198\\ \\ A_{polygon}=220cm^2[/tex]
Learn more about the area of compound shapes here:
brainly.com/question/15884960
