A circle is the most recognizable shape in geometry and finding its area is tricky. Learning how to find the area of a circle is essential as it helps to determine real-life situations like the size of round rug needed or to calculate the space required to construct a garden which is round in shape. The circles are ellipses that have a radius which is constant around its center, and they have properties like diameter, radius, area, and circumference.
Area of a Circle:
The formula used to determine the area of a circle is A = πr2.
A π is a non-algebraic number which is the ratio of the circumference to its diameter and is estimated at 3.14. To find the area of a circle, you should multiply the radius by radius and then multiply by 3.14.
To find the Radius of a Circle: A radius is measured from the center to the edge of a circle. The length of the radius will remain the same irrespective of it being measured in any direction. The diameter is twice the radius, and it is a line that passes through the center and divides the circle into two halves and connects the opposite sides of the circle. Generally, to calculate the area of a circle, the radius will be provided. For example, if the radius if a circle is 4 cm, using the above formula
A = π_r_2.
Where r is the radius, in the above example, r = 4 and if that is squared then r squared = 4 square = 16.
Multiply by π which is approximated to 3.14. The area of the circle of a radius of 4 cm is
A = 3.14* 16 = 50.24
Calculating using the Diameter: Sometimes, instead of providing radius you will be given the diameter of a circle. If the diameter is provided as 8 cm, then the radius can be determined as the diameter is twice the radius. If the value of the diameter is given, then the radius is ½ of diameter. In the example, then radius = d/2 = 8/2 = 4.
After converting the diameter into the radius, you can now use the previous formula of A = π_r_2. Use the value of the radius determined using the diameter to calculate the area of the circle.
Calculating using the Circumference: If the circumference of a circle is provided, then you can find the area even if the radius is not available.
A = π [C / (2 π)]2.
The circumference is pi multiplied by the diameter. If c is the circumference and d is the diameter then c = πd. The diameter is twice the radius, combine all these qualities to create the following equation.
C = 2πr
r = c/2π
The area of the circle is A = πr(square)
A = square(π(c/2π))
A = square(c)/4π
Circles have various properties like circumference, diameter, radius, and area but finding the radius of the circle helps calculate all the other parameters. Some real-life applications where the area of a circle can be used are the size of the cake and pizza are determined by the diameter of the pan they are baked in and the measurement of the football field and the stadium. Knowing the radius of the circle all the other characteristics can be calculated based on the parameters of the circle many real-life applications are built.