Question

This trapezoid has been divided into two right triangles and a rectangle.

Answer 1

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:

1. Identify the basic shapes;
2. Calculate your individual areas;
3. 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 - $A_{triangle}=\frac{b*h}{2}$. The figure shows:

        b= length of the base= 2in

        h=height=9 in

        Then,  $A_{triangle}=\frac{b*h}{2}=\frac{2*9}{2} =\frac{18}{2}=9 in^2$

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- $A_{rectangle}={b*h}$. The figure shows:

         b= length of the base= 12 in

         h=height= 9in

        Then,  $A_{rectangle}={b*h}=12*9=108 in^2$ .

• STEP 4 - Find the area of the trapezoid.

         $A_{trapezoid}=2*A_{triangle}+1*A_{rectangle}\\ \\ A_{trapezoid}=2*9+1*108\\ \\ A_{trapezoid}=18+108\\ \\ A_{trapezoid}=126in^2$

Learn more about the area of compound shapes here:

brainly.com/question/15884960