Question

Find the area of the shaded region of the following figure, if the diameter of the circle with centre O is 28 cm and​

Answer 1

• given diameter of the circle is 28cm

So

$radius = \frac{d}{2} = 14cm$

First we have to find the radius of the smaller semicircle and the length of the chord PT✓

So, radius of the semicircle = ½ of UT

=> Radius=½×7= 3.5 cm✓

And the length of the chord is TO+OP

$length \: of \: the \: chord \: is \: (14 + 7) = 21cm$

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Now let us find the area of the shaded regions ✓

Ar(semicircle)=

$\frac{1}{2} \times \pi \: r ^{2} \\ \\ we \ \:have \: r = 3.5 \: cm \\ \\ = > area = \frac{3.14 \times 3.5 \times 3.5}{2} \\ \\ = > area = \frac{38.4}{2} \\ \\ = > area = 19.2cm ^{2}$

Now again we have to find the area of the semicircle PFT

$area = \frac{1}{2} \times \pi \: \times r ^{2} \\ \\ (radius \: in \: this \: case = \frac{21}{2} = 10.5cm) \\ \\ = > area = \frac{3.14 \times 10.5 ^{2} }{2} \\ \\ = > area = \frac{346.18}{2} \\ \\ = > area = 173.09cm ^{2}$

• So total shaded area is

(173.09+19.2)cm²

Total area = 192.29 cm²