the figure APB and AQD are semi circle of diameter 7cm each , while ARC and BSP semicircles diameter 14cm each. find the area of shaded region. use=22/7
Answers
The area of the shaded region is 115.5 cm².
Step-by-step explanation:
It is given that,
The diameter of semicircle APB & CQD = 7 cm
The diameter of semicircle ARC & BSD = 14 cm
From the figure attached below, we have,
Step 1:
For the semicircle ARC or BSD:
Diameter, AC = BD = 14 cm
So, radius = 14/2 cm = 7 cm
∴ Area of the semicircle ARC or BSD = ½ * πr² = ½ * 22/7 * 7 * 7 = 77 cm² …… (i)
For the semicircle APB or CQD:
Diameter, AB = CD = 7 cm
So, radius = 7/2 cm
∴ Area of the semicircle APB or CQD = ½ * πr² = ½ * 22/7 * 7/2 * 7/2 = 19.25 cm² …… (ii)
Subtracting (ii) from (i), we get
The area of the shaded region ARCBP or BSDQ = 77 – 19.25 = 57.75 cm²
Step 2:
Now,
The area of the total shaded region in the figure will be given by,
= [area of the shaded region ARCBP] + [area of the shaded region BSDQ]
= 57.75 + 57.75
= 115.5 cm²
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Also View:
In the given fig, APB and CQD are semi circles of diameter 7 cm each, while ARC and BSD are semicircles of diameter 14 cm each. Find the perimeter of the shaded region. (Use π = 22/7)
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Step-by-step explanation:
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