ABCD is a square. A circle is inscribed in the square. Also taking A, B, C, D (the vertices of square) as the centres of four quadrants, drawn inside the circle, which are touching each other on the midpoints of the sides of square. Area of square is 4 cm2 . What is the area of the shaded region?
Answers
Given : ABCD is a square. A circle is inscribed in the square. taking A, B, C, D circles are drawn inside square touching each other on the midpoints of the sides of square. Area of square = 4 cm²
To find : area of the shaded region
Solution:
Area of the square = 4 cm²
Area of square = Side²
=> Side² = 4 cm²
=> Side of the square = 2 cm
A , B , C & D are center of circle
& they are touching each other on the midpoints of the sides of square.
=> Radius of Circle = Side of square/2
=> Radius of Circle = 2/2 = 1 cm
Square has all angles 90°
area of each circle inside square = (90/360)π (Radius)²
= (1/4) π (1)²
= π/4
Area of 4 circles inside square = 4 (π/4) = π cm²
area of the shaded region = Area of square - area of circles inside Square
= 4 - π cm²
= 0.86 cm²
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