write the area of semicircle of diameter 'd'
Answers
Answer:
In the case of a circle, the formula for area, A, is A = pi * r^2, where r is the circle's radius. Since we know that a semicircle is half of a circle, we can simply divide that equation by two to calculate the area of a semicircle. So, the formula for the area of a semicircle is A = pi * r^2/2.
The required area of semicircle will be π(d²)/8 unit².
Given: Diameter of a semicircle = d
To find: The area of semicircle of diameter ‘d’.
Solution:
We know,
Formula for area of a circle = πr²
Where, 'r' is the radius of the circle.
We also know that,
Radius, r = half of the diameter of the circle i.e. d/2
Therefore,
The area of a circle with diameter ‘d’ = π(d/2)²
= π(d²)/4
∴ The area of a circle with diameter ‘d’ is π(d²)/4
And,
Area of a semicircle of diameter ‘d’ = ½ × area of the circle with diameter ‘d’
= ½ × π(d²)/4
= π(d²)/8
∴ The area of the semicircle with diameter ‘d’ is π(d²)/8
Thus, the area of semicircle of diameter ‘d’ is π(d²)/8 unit².
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