Question

how to derive the formula to find area and circumference of a semi-circle, quadrant and 3/4th of a circle?

Answer 1

Formula for area of a circle-$\pi r ^{2}$
semi circle is half of a circle
quadrant is one fourth of a circle
three fourth is three fourth of a circle.
therefore area of semi circle =1/2\pi r ^{2}
therefore area of quadrant = 1/4\pi r ^{2}
area of three fourth=3/4\pi r ^{2}
circumference of a circle =$2 \pi r$
therefore circumference of semi circle=1/2 x 2 \pi r= \pi r
therefore circumference of quadrant = 1/4 x 2 \pi r=\pi r/2
circumference of three fourth= 3/4 x  2 \pi r=3/2\pi r