Question

Ek rectangular field ka length 20m, breath 10m. Ek goat ko field ke corner pr ek rassi se bandha gaya rassi ki length 11m hai to bina chare part ka area=?

Answer 1

If we Imagine the Rectangular Field and The Goat tied at One Corner of the Rectangular Field with Rope of 11 m, We can Notice that : The Area of the Rectangular Field that the Goat can Graze is Equal to the Area of One Quarter of the Circle with Radius of 11 m.

Now, Let us Find the Area of Quarter of Circle which the Goat can Graze :

We know that : Area of Quarter of Circle is given by : $[\frac{\pi r^2}{4}]$

Given : The Length of the Rope = 11 m

⇒ Radius of the Quarter of Circle = 11 m

⇒ Area of Rectangular Field that Goat can Graze = $[\frac{\pi \times 11^2}{4}]$

⇒ Area of Rectangular Field that Goat can Graze = 95 m²

Now, Area of Rectangular Field which Goat cannot Graze is obtained by Subtracting Area of Quarter of Circle that Goat can Graze from the Area of Total Rectangular Field

We know that : Area of Rectangle is given by : Length × Breadth

⇒ Area of Rectangular Field = (20 × 10) = 200 m²

⇒ Area of the Rectangular Field that Goat cannot Graze is :

⇒ (200 - 95) m²

⇒ 105 m²