Answer:
- The area of the figure will be 5π/2 in².
- The perimeter will be 3π + 2 in
Step-by-step explanation:
This figure is a combination of two semi-circles.
- One having diameter of 2 inches i.e. AD
- Other having diameter of 4 inches i.e. AC
As
![{\displaystyle \pi ={\frac {C}{d}}}](https://tex.z-dn.net/?f=%7B%5Cdisplaystyle%20%5Cpi%20%3D%7B%5Cfrac%20%7BC%7D%7Bd%7D%7D%7D)
![{{{C}}}=\displaystyle \pi.d](https://tex.z-dn.net/?f=%7B%7B%7BC%7D%7D%7D%3D%5Cdisplaystyle%20%5Cpi.d)
Perimeter of the big figure could be computed by cutting the perimeters of each circle in half, and then combing them together.
Area could be computed using the same way.
<u>Calculating the Perimeter:</u>
- As the circumference of the smaller circle is 2π in. Cutting it half would yield the circumference of the smaller semi-circle i.e. π.
- As the circumference of the bigger circle is 4π in. Cutting it half would yield the circumference of the bigger semi-circle i.e. 2π.
- As the length of the segment DC is 2 in.
So, the total perimeter would be: π + 2π + 2 = 3π + 2 in
<u>Calculating the Area</u>
Area could be computed using the same way as we did during measuring perimeter.
As the area of circle is
![A={\displaystyle \pi.r^{2}](https://tex.z-dn.net/?f=A%3D%7B%5Cdisplaystyle%20%5Cpi.r%5E%7B2%7D)
As we are dealing with semi-circles. So, cutting the diameters of two semi-circles in half can let us find the radii of them.
So,
- Smaller semi-circle has 1 in radius
- Larger semi-circle has 2 in radius
Areas would have to be cut in half as well, as we are dealing with semi-circles.
So,
For smaller:
![A_{small} =\frac{1}{2} {\displaystyle \pi.r^{2}](https://tex.z-dn.net/?f=A_%7Bsmall%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%20%7B%5Cdisplaystyle%20%5Cpi.r%5E%7B2%7D)
![A_{small} =\frac{1}{2} {\displaystyle \pi.(1)^{2}](https://tex.z-dn.net/?f=A_%7Bsmall%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%20%7B%5Cdisplaystyle%20%5Cpi.%281%29%5E%7B2%7D)
![A_{small} =\frac{1}{2} {\displaystyle \pi](https://tex.z-dn.net/?f=A_%7Bsmall%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%20%7B%5Cdisplaystyle%20%5Cpi)
Hence, the area of smaller will be: π/2 in²
For larger:
![A_{larger} =\frac{1}{2} {\displaystyle \pi.r^{2}](https://tex.z-dn.net/?f=A_%7Blarger%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%20%7B%5Cdisplaystyle%20%5Cpi.r%5E%7B2%7D)
![A_{larger} =\frac{1}{2} {\displaystyle \pi.(2)^{2}](https://tex.z-dn.net/?f=A_%7Blarger%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%20%7B%5Cdisplaystyle%20%5Cpi.%282%29%5E%7B2%7D)
![A_{larger} =2 \pi^{}](https://tex.z-dn.net/?f=A_%7Blarger%7D%20%3D2%20%5Cpi%5E%7B%7D)
Hence, the area of larger will be: 2π in²
Combining them together:
![\frac{1}{2} {\displaystyle \pi^{} + 2 {\displaystyle \pi^{}=\frac{5}{2} {\displaystyle \pi^{}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%7B%5Cdisplaystyle%20%5Cpi%5E%7B%7D%20%2B%202%20%7B%5Cdisplaystyle%20%5Cpi%5E%7B%7D%3D%5Cfrac%7B5%7D%7B2%7D%20%7B%5Cdisplaystyle%20%5Cpi%5E%7B%7D)
Therefore,
- The area of the figure will be 5π/2 in².
- The perimeter will be 3π + 2 in
<em>Keywords: radius, area, perimeter, semi-circle, circle, diameter, circumference of circle</em>
<em>Learn more about circle measurements from brainly.com/question/3855576</em>
<em>#learnwithBrainly</em>