Answer:
The area of the figure be 137.76 units and perimeter of the figure be 42.39 units .
Step-by-step explanation:
Formula
[tex]Perimeter\ of\ a\ semi\ circle = \frac{2\pi\ r}{2}[/tex]
[tex]Area\ of\ a\ circle = \frac{\pi\ r^{2}}{2}[/tex]
Where r is the radius of circle .
As the figure given in the question consist of one big and Three small semicircle .
As
[tex]Radius\ of\ big\ semicircle = \frac{AB+BC+CD}{2}[/tex]
As AB = BC = CD = 6
[tex]Radius\ of\ big\ semicircle = \frac{18}{2}[/tex]
= 9 units
[tex]Radius\ of\ small\ semicircle = \frac{3}{2}[/tex]
= 1.5 units
[tex]\pi = 3.14[/tex]
[tex]Perimeter\ of\ figure = Perimeter\ of\ Big\ semicircle + Perimeter\ of\ three\ semicircle[/tex]
[tex]Perimeter\ of\ figure = 9\times 3.14+3 \times 3.14\times 1.5[/tex]
= 28.26 + 14.13
= 42.39 units
[tex]Area\ of\ figure = Area\ of\ Big\ semicircle + Area\ of\ three\ semicircle[/tex]
[tex]= \frac{3.14\times 9\times 9}{2} + 3 \frac{3.14\times 1.5\times 1.5}{2}[/tex]
Area of the figure = 127.17 + 10.59
= 137.76 units
Therefore the area of the figure be 137.76 units and perimeter of the figure be 42.39 units .
Answer:
Total area of shaded region is [tex]54 \pi}[/tex]
Total perimeter of figure is [tex]18 \pi[/tex]
Step-by-step explanation:
Area of semi circle =[tex]\frac{1}{2} \pi r^2[/tex]
Perimeter of semi circle =[tex] \pi r[/tex]
Consider the given figure , it has 4 semi-circles with diameter AD , AB, BC, CD.
We have to determine the shaded area ,
First consider , Semi circle with diameter AD,
diameter AD = 6 + 6 + 6 = 18 cm
Radius is half of diameter.
Radius = 9 cm
Thus, area of semi circle with diameter 18 cm is,
Area of semi circle =[tex]\frac{1}{2} \pi (9)^2=\frac{81 \pi}{2}[/tex] .....(1)
Area of 3 semi circles with diameter 6 cm = 3 × Area of semi circles with diameter 6 cm
diameter = 6 cm ⇒ Radius = 3 cm
Area of semi circle =[tex]\frac{1}{2} \pi (3)^2=\frac{9 \pi}{2}[/tex] .....(2)
Area of 3 semi circles with diameter 6 cm = 3 × Area of semi circles with diameter 6 cm
[tex]=\frac{3 \times 9 \pi}{2}[/tex]
[tex]=\frac{27 \pi}{2}[/tex] ..........(3)
Total area of shaded region = Area of semi circle with diameter 18 cm + Area of 3 semi circles with diameter 6 cm
=[tex]\frac{81\pi}{2}+\frac{27 \pi}{2}[/tex]
=[tex]\frac{(81+27) \pi}{2}=\frac{108 \pi}{2}[/tex]
Thus, Total area of shaded region is [tex]54 \pi}[/tex]
Perimeter of the semi circle with radius 9 cm
Perimeter of semi circle =[tex] \pi r=9 \pi[/tex]
Perimeter of the one semi circle with radius 3 cm
Perimeter of semi circle =[tex] \pi r=3 \pi[/tex]
Perimeter of the 3 semi circle with radius 3 cm = 3 × Perimeter of the one semi circle with radius 3 cm
[tex]=9 \pi[/tex]
Total perimeter of figure is [tex]9 \pi+9 \pi=18 \pi[/tex]
