Area of the square inscribed in the semicircle.

If the area of a square inscribed in a circle is 15 cm2 , then the area (in cm2) of the square inscribed in the semicircle of the same circle is

  1. 6
  2. 5
  3. 3.75
  4. 7.5

 

Manish Listener Asked on 28th October 2014 in Maths.
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1 Answer(s)

Answer :  6

Let pqrs be the square in full circle with sides a.
given area = a^2 = 15 cm^2
Then, sq= diameter=2*radius
a^2 + a^2 = (2*radius)^2
2a^2 = 4 * radius^2
a^2 = 2 *radius^2
radius^2 = 15/2                     ——- (i)
Let pqrs be the square in half circle. with side x.
If we produce a mirror image of the semicircle then we get a circle and a rectangle inscribed in it.
Length of rect = 2x and Breadth of rect. = x.
Diagonal= Diameter = 2*radius

Now, (2x)^2 + x^2 = (2*radius)^2
4x^2+x^2 = 4*radius^2
5x^2 = 4*radius^2
x^2 = (4*radius^2 )/5
x^2 = (4*15/2)/5                                     [from equation i]
x^2 =

Hence area of square in semicircle = 6 cm^2

KumarDilip Newbie Answered on 8th August 2015.
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