From figure shows that the polygon is composed of a triangle, a square and a trapezoid. The area of the irregular figure is 47.
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.
- STEP 1 - Identify the basic shapes.
The polygon is composed of a triangle, a square and a trapezoid. See the attached image.
Therefore, you should sum the area of these geometric figures for determining the area of the irregular figure.
- STEP 2 - Find the area of the triangle.
Area of the triangle -[tex]\frac{bh}{2}[/tex] . The figure shows:
b= length of the base= 5
h=height=4
Then, [tex]A_{triangle}=\frac{bh}{2} =\frac{4*5}{2} =\frac{20}{2} =10[/tex]
- STEP 3 - Find the area of the square.
Area of the square -[tex]l^2[/tex] . The figure shows:
l= length of the side= 5
Then, [tex]A_{square}=l^2 =5^2=25[/tex]
- STEP 4 - Find the area of the trapezoid.
Area of the trapezoid - [tex]\frac{(B+b)*h}{2}[/tex] . The figure shows:
B= long base= 5
b= short base= 3
h=height=3
Then, [tex]A_{trapezoid}=\frac{(5+3)*3}{2}=\frac{(8)*3}{2}=\frac{24}{2} =12[/tex]
- STEP 5 - Find the area of the polygon.
[tex]A_{polygon}=A_{triangle}+A_{square}+A_{trapezoid}\\ \\ A_{polygon}=10+25+12\\ \\ A_{polygon}=47[/tex]
Learn more about the area of compound shapes here:
brainly.com/question/15884960
