Answer:
A) (6π + 10) m^2
Step-by-step explanation:
The area of the composite figure = (Bigger half circle - Smaller half circle) + Area of the rectangle
Area of half circle = (πr^2) /2
Area of a rectangle = length * width
= (π.4^2 / 2 - π(2)^2 / 2) + 5*2
= π (16/2 - 4/2) + 10
= π(8 - 2) + 10
= π6 + 10
Area of the composite figure = (6π + 10)m^2
Answer is A) (6π + 10) m^2
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Answer:
Option A) [tex](6\pi + 10)~ m^2[/tex]
Step-by-step explanation:
We are given a composite figure. We have to find the area of the composite figure.
The area of figure =
[tex]\frac{1}{2}(\text{Area of bigger circle - Area of inner circle}) + \text{Area of rectangle}[/tex]
[tex]\text{\bold{Area of outer circle}} = \pi R^2\\\text{where R is the radius of outer circle}\\= \pi (4)^2 = 16\pi~ m^2\\\text{\bold{Area of inner circle}} = \pi r^2\\\text{where r is the radius of inner circle}\\= \pi (2)^2 = 4\pi~ m^2\\\text{\bold{Area of Rectangle}} = l\times b\\\text{where l is the length and b is the breadth of the rectangle}\\= 5\times 2 = 10~m^2[/tex]
[tex]\text{Area of composite figure} = \\\frac{1}{2}(\text{Area of bigger circle - Area of inner circle}) + \text{Area of rectangle} = 8\pi - 2\pi + 10\\=(6\pi + 10)~ m^2[/tex]
Option A) [tex](6\pi + 10)~ m^2[/tex]
