Test your skills in geometry with this quiz question.
In the picture below you will see a square inside a square.
The inside square is drawn from the midpoints of all the four sides of the square.
Inside this square there is a circle.
Can you find the area of the square?
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From the given information we know that the inside square is drawn from the mid points of the sides of the outer square.
So the right angled triangle formed will have its sides as 4m.
To find the diagonal value which is also the side of the inside square, we can use the Pythagoras theorem;
(Inside square sides)^2 = 4^2 + 4^2 = 16 + 16 = 32
inside square sides = 4√2
inside square side = diameter of the circle = 4√2
So radius of the square = 2√2
Area of circle = π x r^2 = π x(2√2)^2 = π x(4 x 2) = 8π
Answer = D. 8π