Question

Find the area of square inscribed in a circle of radius 10 cm?​

Answer 1

Answer:

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Step-by-step explanation:

When a square is inscribed inside a circle, the diagonal of square and diameter of circle are equal. Further, if radius is 1 unit, using Pythagoras Theorem, the side of square is √2

Now as radius of circle is 10, are of circle is π×10×10=3.1416×100=314.16

and as the radius is 10, side of square is 10√2 and area of square is

(10√2)2=10×10×2=200

and area of the circle not covered by the square is 314.16−200=114.16 units

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

• Radius of circle is 10 cm

• A square is inscribed in the circle.

Since,

➢ Radius of circle = 10 cm

So,

➢ Diameter of circle = 2 × Radius = 2 × 10 = 20 cm

Now,

➢ As Square is inscribed in a circle.

➢ So, Diagonal of inscribed square = Diameter of circle.

➢ It means, Diagonal of square = 20 cm

We know,

$\purple{\rm :\longmapsto\:\boxed{\tt{ \: \: Area_{(square)} \: = \: \frac{1}{2} \times {(diagonal)}^{2} \: \: }}}$

So,

$\rm :\longmapsto\:Area_{(square)} = \dfrac{1}{2} \times {(20)}^{2}$

$\rm :\longmapsto\:Area_{(square)} = \dfrac{1}{2} \times 400$

$\bf\implies \:Area_{(square)} = 200 \: {cm}^{2}$

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$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$