The area of the triangle on left is in²: 9
The area of the triangle on the right is in²: 9
The area of the rectangle is in²: 108
The area of the trapezoid is in²: 126
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.
This trapezoid is composed of two triangles 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{b*h}{2}[/tex]. The figure shows:
b= length of the base= 2in
h=height=9 in
Then, [tex]A_{triangle}=\frac{b*h}{2}=\frac{2*9}{2} =\frac{18}{2}=9 in^2[/tex]
Note that the triangles are equals, consequently, they present the same values for the area.
- STEP 3 - Find the area of the rectangle.
Area of the rectangle- [tex]A_{rectangle}={b*h}[/tex]. The figure shows:
b= length of the base= 12 in
h=height= 9in
Then, [tex]A_{rectangle}={b*h}=12*9=108 in^2[/tex] .
- STEP 4 - Find the area of the trapezoid.
[tex]A_{trapezoid}=2*A_{triangle}+1*A_{rectangle}\\ \\ A_{trapezoid}=2*9+1*108\\ \\ A_{trapezoid}=18+108\\ \\ A_{trapezoid}=126in^2[/tex]
Learn more about the area of compound shapes here:
brainly.com/question/15884960
