Question

find area of the square whose vertices lies on the circle of radius 20 CM. explain with diagram. ​

Answer 1

Step-by-step explanation:

SINCE THE SQUARE IS INCCRIBED IN A CIRCLE SO ITS DIAGONAL = CIRCLE'S RADIUS

SO, DIAGONAL = 20 cm .

NOW , SINCE , DIAGONAL = √2 SIDE OF SQUARE

So, SIDE = 20 / √2 = 10√2 cm

SO AREA OF SQUARE = SIDE² =( 10√2 )² = 200 cm²

Answer 2

Required area of the square is 800 cm²

Step-by-step explanation:

Given : Radius of circle = 20 cm

Therefore diameter of circle = 2 x 20 = 40 cm

As can be seen in figure the diameter of circle is diagonal of square

Now as we know

$\sqrt{2}\text { Side of Square }= \text{ Diagonal of square }$

So

$\sqrt{2} \times Side = 40 \\\\\Rightarrow side= \dfrac{40}{\sqrt{2} } \\\\\Rightarrow side= \dfrac{40}{\sqrt{2} }\times \dfrac{\sqrt{2} }{\sqrt{2} } =\dfrac{40\sqrt{2} }{2 }=20\sqrt{2} cm$

Now as we know area of square is given by

$area=a^2$ where a is the side of square

Therefore

$area=(20 \sqrt{2} )^2=800 cm^2$

Hence, required area of the square is 800 cm²

#Learn more

Find area of the square whose diagonal is 20 cm​

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