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In Fig. 11.5, a square of diagonal \[8\] cm is inscribed in a circle. Find the area of the shaded region.
In Fig. 11.5, a square of diagonal \[8\] cm is inscribed in a circle. Find the area of the shaded region.
Areas Related to Circles | Exercise 11.3 | Maths | NCERT Exemplar
In Fig. 11.5, a square of diagonal \[8\] cm is inscribed in a circle. Find the area of the shaded region.

Let us take a be the side of square.

From the question we got, diagonal of square and diameter of circle is \[8\] cm

In right angled triangle ABC,

By Using Pythagoras theorem we got,

\[{{(AC)}^{2}}={{(AB)}^{2}}+{{(BC)}^{2}}\]

∴ \[{{(8)}^{2}}={{a}^{2}}+{{a}^{2}}\]

⇒ \[64=2{{a}^{2}}\]

⇒ \[{{a}^{2}}=32\]

Hence,

area of square = \[{{a}^{2}}=32\]\[c{{m}^{2}}\]

∴ Radius of the circle = \[Diameter/2\] = \[4\]cm

∴ Area of the circle = \[\pi {{r}^{2}}\] = \[\pi {{(4)}^{2}}\]= \[16\pi \]\[c{{m}^{2}}\]

Therefore, the area of the shaded region = Area of circle of radius r – Area of square of side a

The area of the shaded region = \[16\pi -32\]

= \[16\times (22/7)-32\]

= \[128/7\]

= \[18.286\] \[c{{m}^{2}}\]

i

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