in the given figure PQ is equal to 7 centimetre QR is equal to 3 cm then find the area of the shaded region
Answers
If PQ is equal to 7 cm & QR is equal to 3 cm then the area of the shaded region is 15.71 cm².
Step-by-step explanation:
It is given that,
PQ = 7 cm = diameter of semicircle PAQ
QR = 3 cm = diameter of semicircle RTQ
Also,
The diameter of the bigger semicircle, PSR = 10 cm (as shown in the figure)
So, Radius of the semicircle PSR, r₁ = 10/2 = 5 cm
And,
Radius of semicircle RTQ, r₂ = 3 cm = 3/2 cm
Radius of semicircle PAQ, r₃ = 7/2 cm
Now,
The area of the shaded region is given by,
= [Area of semicircle PSR] + [Area of semicircle RTQ] + [Area of semicircle PAQ]
= [½ * πr₁²] + [½ * πr₂²] + [½ * πr₃²]
= ½ * π * (r₁ + r₂ + r₃)
Substituting the values of r₁, r₂ & r₃
= ½ * 22/7 * (5 + 3/2 + 7/2)
= ½ * 22/7 * [(10+3+7)/2]
= ½ * 22/7 * 10
= 22/7 * 5
= 15.71 cm²
Thus, the area of the shaded region is 15.71 cm².
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