Question

3. Rani bought a new field that is next to one she already owns (see theFig.). This field is in the shape of a square of side 70 m. She makes asemi-circular lawn of maximum area in this field.
(i) Find the perimeter of the lawn.
(ii) Find the area of the square field excluding the lawn.​

Answer 1

70 multiple by 4 and it's answer will be 280m

Answer 2

$\huge \bf {Question}$

Rani bought a new field that is next to one she already owns (see the fig.). This field is in the shape of a square of side 70 m. She makes a semicircular lawn of maximum area in this field.

(i) Find the perimeter of the lawn.

(ii) Find the area of the square field excluding the lawn.

$\huge \bf {Answer}$

Given:-

• Side of Square = 70m.

To Find:-

1. Find the Perimeter of the lawn.
2. Find the area of the square field excluding the lawn.

We know:-

Side of Square = Diameter of semicircle = 70m.

So, Radius of lawn = 35m.

$\huge \sf \orange{\underline{\underline {Part\: 1.}}}$

Perimeter of the lawn = semi perimeter of circle + diameter

$\longrightarrow$ $\sf {π(\dfrac{70}{2})+70}$

$\longrightarrow$ $\sf {\dfrac{22}{7}×35+70}$

$\longrightarrow$ $\sf {22×5+70}$

$\boxed {\sf {\green {180m.}}}$

$\huge \sf \orange {\underline{\underline{Part\: 2.}}}$

${\boxed {\sf {\green {Area\: of\: Square = Side\: \times Side}}}}$

Area of Square = 70 × 70 = $\sf {4900m}{2}$

The area of the square field excluding the lawn = Area of square - area of semicircle

$\longrightarrow$${\sf {4900 - \frac {1}{2} π {r}^{2}}}$

$\longrightarrow$$\sf {4900 - \frac {1}{2} \times \frac{22}{7} \times {35}^{2}}$

$\longrightarrow$$\sf {4900 - 1925}$

${\boxed {\sf {\green {{2975m}^{2}}}}}$