Question 1187599
the radius of the garden is 20 meters.
the circumference of the garden is 2 * pi * r = 40 * pi.
the area of the garden is pi * r^2 = pi * 20^2 = 400 * pi.


the arc is 15 * pi.


the central angle of the arc is 15 * pi / (40 * pi) * 360 = 135 degrees.


the area of the sector is equal to 135/360 * 400 * pi = 150 * pi.


the circumference and the area of the sector of the circle are proportion to the central angle of the sector divided by 360 * the circumference of the circle and also times the area of the circle.


when the central angle of the sector is 135 degrees, then the fraction is 135/360.


the circumference of the circle is 2 * pi * 20 = 40 * pi.
the area of the circle is pi * 20^2 = 400 * pi.


the arc of the sector is 135 / 360 * 40 * pi = 15 * pi.
this is not surprising since we used the circumference of the circle and the length of the arc to find the central angle.


the area of the sector is 135 / 360 * 400 * pi = 150 * pi.


here's a reference on arc length of a sector and area of a sector.


<a href = "https://byjus.com/maths/sector-of-a-circle/" target = "_blank">https://byjus.com/maths/sector-of-a-circle/</a>