Question

Two goats are tethered to diagonally opposite vertices of a field formed by joining the mid-points of the adjacent sides of another square field of side 20 √2 m. What is the total grazing area of the two goats?

(a) 100 π m² 

(b) 50 (√2− 1) π m² 

(c) 100 π (3 − 2√2) m² 

(d) 200 π (2 − √2) m²

Answer 1

Answer : (a) 100 π m² 

ABCD is the original square, the mid-points of whose sides are joined to give the square PQRS.

Let the goats be tethered at points P and R or Q and S. 

Then, the length of the rope = 10 √2 m. 

∴ The two goats together will graze an area equal to the area of a semi-circle with a radius of 10 √2 m.

∴ Total area grazed = \(\frac{\pi r^2}{2}\) = \(\frac{\pi \times (10\sqrt{2})^2}{2}\) 

= 100 π m².