Question

A farmer had a square field of side 150 m. He divided this field between his son and daughter
so that he gave all the four corners in the form of four sectors of circles of radius 49 m each
to his daughter and an equal amount of area to his son. The remaining area he left for
charitable purposes. Find out the area he left for charity. What values of the farmers are
depicted through this action ? (Use =
SIN

Answer 1

Side of square = 150 m

Area of sqaure = a²

$\bf \Longrightarrow 150 \times 150 \\ \\ \large \underline{ \boxed{\bf \red{ Area \: of \:square= 22500 \: {m}^{2}}}}$

Radius of sector = 49 m

Angel of sector = 90°

$\underline{\boxed{ \bf \blue{Area \: of\: Sector = \pi {r}^{2} \times \frac{ \theta}{360}} } }\\ \\ \bf area = \frac{22}{7} \times 49 \times 49 \times \frac{90}{360} \\ \\ \bf area = 22 \times 49 \times 7 \times \frac{1}{4} \\ \\ \large\underline{ \boxed{\orange{ \bf Area \: of \: sector = 1886.5 {m}^{2}}}}$

There are 4 such sector so multiply this by 4

$\bf 1886.5 \times 4 = 7546 \: {m}^{2}$

Area of remaining field :

Area of square - Area of 4 sectors

22500 - 7546 = 14954 m²

$\large \underline{ \boxed{ \green{\bf Area \: of \: charity \: field = 14954{m}^{2}}}}$