the perimeter of a circle is 220 cm. The area of a square inscribed in it is....
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From the properties of circle, We know : -
• Circumference of circle = 2πr, where r is the radius of the circle.
Now, comparing the circumference of the circle with the formula given above,
= > 2πr = 220 cm
On onbserving ( the diagram ), we get :
Diameter is same is the diagonal of the square.
Therefore,
Diagonal of square = Diameter of circle
Diagonal of square = 2 x radius = 2 x 35 cm = 70 cm
Now,
Let the side of the square be a cm,
By Pythagoras Theorem :
= > ( side )² + ( side )² = ( diagonal )²
= > a² + a² = ( 70 cm )²
= > 2a² = 4900 cm²
= > a² = 2450 cm²
Now,
a² = 2450 cm² = ( side )² = Area of square.
Therefore,
Area of the square is 2450 cm^2
Verified answer
→Perimeter=Circumference of circle→Circumference=220cm
→C=2πr
→220=2×22/7×r
→220×7/44=r
→35=r
→d=2r
→d=2×35
→d=70cm
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Diameter of circle=Diagonal of square
Let side of square be x
Using Pythagoras theorem
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→x²+x²=70²
→2x²=4900
→x²=2450
→x=√2450
→x=49.49cm²
Area=S×S
Area=2449.20=2450cm²