Question

This composite figure is created by placing a sector of a circle on a rectangle. What is the area of this

Answer 1

The area of the composite figure is 29.92 m².

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.

      The figure of the question as informed is composed for a sector of circle and a rectangle. Therefore, you should sum the area of these geometric figures.

• STEP 2 - Find the area of the sector of circle.

           Area of the sector of circle= $\frac{\theta \cdot \pi }{360}\cdot r^2$, where:

           r= 5.5 m

           Θ=30°

         Then,

                       $\frac{\theta \cdot \pi }{360}\cdot r^2\\ \\ \frac{\;30\cdot \pi }{360}\cdot 5.5^2=7.92 m^2$

• STEP 3 - Find the area of the rectangle.

      Area of the rectangle=$b*h$ . The figure shows:

        b= length of the base= 5.5 m

        h=height= 4 m

       Thus, the area of the rectangle=$5.5*4=22m^2$  .

• STEP 4 - Find the composite figure

       $A_{composite\; figure}=A_{sector\; circle}+A_{rectangle}\\ \\ A_{composite\; figure}=7.92+22=29.92\; m^2$

Learn more about the area of compound shapes here:

brainly.com/question/15884960