Find the Area

Geometry Level 2

A B C ABC is a circle having a radius of 2 meter. A square E F G H EFGH is attached into it.

Find the area of the square E F G H EFGH .


The answer is 8.

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Shamim Hasan by Shamim Hasan , 26, Japan

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5 solutions

Shamim Hasan
Apr 17, 2014

The diagonal of the square must be as same as the diameter of the circle which is 2 x 2 = 4 . So the length of the square is 4 ÷ √2 = 2√2 .. so the area of the square is (2√2)² = 8 sq. meter

7 Helpful 0 Interesting 0 Brilliant 0 Confused
Eric Kim
May 23, 2014

We know that the formula to find the area of a square/diamond is 1/2 * d^2 which d is the diagonal or the diameter in this case. 1/2 * 4 * 4=8! :)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

OC=OH=radius=2cm. Thus length of diagonal, d = 4cm. Area of square = (d^2)/2=8cm^2

1 Helpful 0 Interesting 0 Brilliant 0 Confused

excellent answer, but the unit here is meter ;)

George Nasry - 7 years ago
Nisha P Mathew
Jun 12, 2014

The diameter of the circle is same as the diagonal of the square.So the diagonal is 4 meter. Then the area of the square is 1/2 (4^2 )=8 sq. meter

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Devendra Sahasi
Jun 9, 2014

consider diagonal EG and FH length of 4 m each the bisect each other at 90 degree ( as its square) now by right triangle E0^2 + OF^2 = EF ^2 4 + 4 = EF^2 EF = 2*root(2) m = side of square

area = EF ^2 = 8 metre sq

hence done :P

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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