Answer:
[tex]Area = 98.2142857143[/tex]
[tex]Perimeter = 39.2857142857[/tex]
Step-by-step explanation:
From the attachment, we have:
- 2 semicircles B and C
- 1 quarter circle CDE
- radius, r = 5cm
To calculate the total area of the figure, we have to calculate the areas of individual shapes, then add them together
For Semicircle B
[tex]Area = \frac{\pi r^2}{2}[/tex]
Substitute 5 for radius (r)
[tex]A_1 = \frac{\pi * 5^2}{2}[/tex]
[tex]A_1 = \frac{\pi * 25}{2}[/tex]
[tex]A_1 = \frac{25\pi}{2}[/tex]
For Semicircle C
[tex]Area = \frac{\pi r^2}{2}[/tex]
Substitute 5 for radius (r)
[tex]A_2= \frac{\pi * 5^2}{2}[/tex]
[tex]A_2 = \frac{\pi * 25}{2}[/tex]
[tex]A_2 = \frac{25\pi}{2}[/tex]
For Quarter circle DC
[tex]Area = \frac{\pi r^2}{4}[/tex]
Substitute 5 for radius (r)
[tex]A_3= \frac{\pi * 5^2}{4}[/tex]
[tex]A_3= \frac{\pi * 25}{4}[/tex]
[tex]A_3= \frac{25\pi}{4}[/tex]
The area of the shape is:
[tex]Area = A_1 + A_2 +A_3[/tex]
[tex]Area = \frac{25\pi}{2}+\frac{25\pi}{2}+\frac{25\pi}{4}[/tex]
Take LCM
[tex]Area = \frac{50\pi+50\pi+25\pi}{4}[/tex]
[tex]Area = \frac{125\pi}{4}[/tex]
Take
[tex]\pi = \frac{22}{7}[/tex]
So, we have:
[tex]Area = \frac{125}{4} * \frac{22}{7}[/tex]
[tex]Area = \frac{125*22}{4*7}[/tex]
[tex]Area = \frac{2750}{28}[/tex]
[tex]Area = 98.2142857143[/tex]
To calculate the total perimeter of the figure, we have to calculate the circumference of individual shapes, then add them together
For Semicircle B
[tex]Circumference = \pi r[/tex]
Substitute 5 for radius (r)
[tex]C_1 = \pi * 5[/tex]
[tex]C_1 = 5\pi[/tex]
For Semicircle C
[tex]Circumference = \pi r[/tex]
Substitute 5 for radius (r)
[tex]C_2 = \pi * 5[/tex]
[tex]C_2 = 5\pi[/tex]
For Quarter circle DE
[tex]Circumference = \frac{\pi r}{2}[/tex]
Substitute 5 for radius (r)
[tex]C_3 = \frac{\pi * 5}{2}[/tex]
[tex]C_3 = \frac{5\pi}{2}[/tex]
The perimeter of the shape is:
[tex]Perimeter = C_1 + C_2 + C_3[/tex]
[tex]Perimeter = 5\pi + 5\pi + \frac{5\pi}{2}[/tex]
Take LCM
[tex]Perimeter = \frac{10\pi + 10\pi + 5\pi}{2}[/tex]
[tex]Perimeter = \frac{25\pi}{2}[/tex]
Take
[tex]\pi = \frac{22}{7}[/tex]
So, we have:
[tex]Perimeter = \frac{25}{2} * \frac{22}{7}[/tex]
[tex]Perimeter = \frac{25*22}{2*7}[/tex]
[tex]Perimeter = \frac{550}{14}[/tex]
[tex]Perimeter = 39.2857142857[/tex]
