Segment of a circle is the part of the circle. The total area of the composite figure is 142.1544 m².
What is the area of the segment of a circle?
The area of the segment of the circle is given by the formula,
[tex]\rm \text{Area of the rectangle} = \pi r^2 \times \dfrac{\theta}{360}[/tex]
As it is given that the composite figure is made up of a circular segment and a rectangle, therefore, we will find the area of the rectangle and the area of the circular segment individually.
Area of the rectangle
The area of the rectangle is the product of its length and breadth, therefore, the area is,
[tex]\rm \text{Area of the rectangle} = Length \times breadth[/tex]
[tex]= 14 \times 6\\\\=84\rm\ m^2[/tex]
Area of the sector of the circle
[tex]\rm \text{Area of the rectangle} = \pi r^2 \times \dfrac{\theta}{360}[/tex]
[tex]= \pi \times 14^2 \times \dfrac{34}{360}\\\\=58.1544\rm\ m^2[/tex]
The total area of the composite figure
The total area of the composite figure
= Area of rectangle + Area of the segment of the circle
= 84 + 58.1544 m²
= 142.1544 m²
Hence, the total area of the composite figure is 142.1544 m².
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