Question

it is proposed to add to a sqyare lawn measuring 50m on a side two circular ends the centre of each circle being the point of intersection of the diagonals of the square find the area of the whole lawn

Answer 1

o is the center of the circular arc CD and AB.
So AC or BD will be the diameter of circle.
In right triangle ABC we have;
AC2=AB2+BC2 (using Pythagorean rule)
⇒AC=AB2+BC2−−−−−−−−−−√=50square+50square−−−−−−−−√⇒AC=50√2
so radius of circular arc CD or AB = 12(50square√2)=600root2cm
Since ∠COD=∠AOB=90°
So area of sector AOB = area of sector COD = 12×90×(600√)2=45×600×2=75690cm2
Area of square = (58×58) cm2
Now Area of whole lawn = Area of sector AOB + Area of sector COD + 12(Area of square)
=75690+75690+12(58×58)=153062 cm2
So Area of whole lawn is 153062 cm2