Abcd is a square with side 2√2 cm and inscribed in a circle find the area of the shaded region π= 3.14
Answers
Answer:
4.56 cm²
1.14 cm²
Step-by-step explanation:
Abcd is a square with side 2√2 cm and inscribed in a circle find the area of the shaded region π= 3.14
Diagonal of square = √((2√2)² + (2√2)²) = √ (8 + 8) = √16 = 4cm
Diameter of Circle = 4 cm
Radius of Circle = 4/2 = 2cm
Area of circle = π r² = 3.14 * (2)² = 12.56 cm²
Area of square = (2√2)² = 8 cm²
Area of circle - Area of square = 12.56 - 8 = 4.56 cm²
Area of one shaded portion = 4.56/4 = 1.14 cm²
The area of the shaded area is 20.52 cm² .
Step-by-step explanation:
Formula
Area of a square = a²
Where a is the side of the square and r is the radius of the circle .
As given
ABCD is a square with side 6 cm.
Now first find out the radius of the circle.
In ΔABC
AC² = AB² + BC²
Now by using the pythagorean theorem
Hypotenuse² = Perpendicular² + Base²
(As AB = BC = 6 cm)
AC² = 6² + 6²
AC² = 36 + 36
AC² = 72
AC = √72
AC = 6√2 cm
Thus the diameter of the circle is 6√2 cm .
Radius = 3√2 cm
Thus
Shaded area = Area of a circle - Area of a square
= 3.14 × 3√2 × 3√2 - 6²
= 3.14 × 9 × √2 × √2 - 36
(As √2 × √2 = 2 , 6² = 36 )
= 3.14 × 9 × 2 - 36
= 56.52 - 36
= 20.52 cm²
Therefore the area of the shaded area is 20.52 cm² .