Question

In the figure, ABCD is a square
Inscribed in a circle. Its perimeter
s 56√2 cm. What is the area of
the shaded region ?
(1) 392 cm (2) 224 cm
(3) 168 cm (4) 324 cm​

Answer 1

❏ Question:-

In fig:(see the questionar attachment)

ABCD is a square

ABCD is a squareInscribed in a circle. Its perimeter is 56√2 cm. What is the area of the shaded region ?

shaded region ?(1) 392 cm.

(2) 224 cm.

(3) 168 cm.

(4) 324 cm.

❏ Solution:-

✦ Given:-

• perimeter of the inscribed square is = 56√2 cm

✦ To Find :-

• Area of the shaded region = ?.

✦ Explanation :-

Now, we know that The Diagonal of a Square inscribed into a circle is the diameter of that circle,

Now,

Let, the side of the square is = a cm.

$\sf \implies 4\times side = perimeter$

$\sf \implies 4\times a= 56\sqrt{2}$

$\sf \implies a= \frac{\cancel{56}\sqrt{2}}{\cancel4}$

$\sf \implies a= 14\sqrt{2}\:cm$

Now,

$\sf \implies \sqrt{2}\times side = Diagonal$

$\sf \implies \sqrt{2}\times 14\sqrt{2}= Diagonal$

$\sf \implies Diagonal=28\:cm$

therefore ,

•diameter(d) of the Circle is =28 cm.

•radius (r) of the Circle is =(28/2)cm=14 cm

Hence, Area of the shaded region is= Area of the circle- area of the inscribed square

$\sf \implies A_{shaded\: region}=A_{circle}-A_{square}$

$\sf \implies A_{shaded\: region}=\frac{22}{7}\times(r)^2-(a)^2$

$\sf \implies A_{shaded\: region}=\frac{22}{7}\times(14)^2-(14\sqrt{2})^2$

$\sf \implies \boxed{A_{shaded\: region}=616-392=224}$

∴Area of the shaded region is = 224 cm²

option (b) 224 cm²

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Answer 2

❏ Solution:-

✦ Given :-

• perimeter of the inscribed square is = 56√2 cm

✦ To Find :-

• Area of the shaded region = ?.

✦Answer:-

∴Area of the shaded region is = 224 cm²