Question

in the given figure PQ is equal to 7 centimetre QR is equal to 3 cm then find the area of the shaded region​

Answer 1

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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Also View:

In the the following figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region.  

https://brainly.in/question/9504720

Find the area of the segments shaded in figure, if PQ = 24 cm., PR = 7 cm. and QR is the diameter of the circle with centre O (Take π = 22/7 )

https://brainly.in/question/5484019