Question

Here is the question

Answer 1

The area is 5π/2 in² and the perimeter is 3π+2 in.

Step-by-step explanation:
The area of a circle is given by the formula A=π*r². The top part of the figure is half a circle that has a radius of 2; this means the area would be
A=(1/2)π*2² = (1/2)π*4 = 2π.

The bottom part of the figure is half a circle with a diameter of 2; since the diameter is twice as long as the radius, this means the radius is 2/2 = 1, and the area would be A=(1/2)π*1² = 1/2 π.

Adding these, we have 2 1/2 π, which can be written as 5π/2.

The perimeter of a circle is the circumference, which is given by the formula C=π*d. The top part has a radius of 2, so the diameter is 2*2=4; this makes the circumference C=1/2(π)(4) = 2π.

The bottom part has a diameter of 2, which makes the circumference C=1/2(π)(2) = 1π.

Together this gives us 3π.

We also must add the length of CD to this; CD=2, which gives us 3π+2.

Answer 2

The upper semicircle ABCD has radius R=2 and area
`A_u= (1)/(2) \pi R^2= (1)/(2) \pi\cdot 2^2=2\pi` and the lower semicircle AD has radius r=1 and area
`A_l= (1)/(2) \pi r^2= (1)/(2) \pi\cdot 1^2= (1)/(2)\pi`. The whole fugure area is
`A=A_u+A_l=2\pi + (1)/(2)\pi= (5)/(2) \pi`.
The perimeter consists of upper semicircle length, lower semicircle length and CD length.

`L_u= (1)/(2) \cdot(2\pi R)=2\pi`

`L_l= (1)/(2) \cdot(2\pi r)=\pi`

`L_(CD)=2`
and the perimeter
`P=L_u+L_l+L_(CD)=2\pi+\pi+2=3\pi+2`