Question

a circular grassland has the perimeter of 660m .a plot in the shape of a square having its vertices on the circumference of the field is marked in the field.calculate the area of the square field.

Answer 1

$\huge\bf\red{\underline{\underline{Given}}}\::$

• $\sf\gray{Perimeter \:of \:circular\: grassland \:= \:660m}$
• $\sf\gray{A\:plot \:in\: the\: shape\: of \:a\: square\: having\: its\: vertices \:on\: the\: circumference \:of \:the\: field\: is \:marked\: in \:the \:field.}$

$\huge\bf\red{\underline{\underline{To\:Find}}}\::$

• $\sf\gray{Area\: of \:the\: square\:field}$

$\huge\bf\red{\underline{\underline{Solution}}}\::$

• $\sf\underline\orange{Perimeter\:=\:660m}$

$\Rightarrow\: \sf\purple{2\pi r\:=\:660}$

$\Rightarrow\: \sf\green{r\:=\:\dfrac{660}{2\pi}}$

$\Rightarrow\: \sf\purple{r\:=\:\dfrac{660\:\times\:7}{2\:\times\:22}}$

$\Rightarrow\: \sf\purple{r\:=\:15\:\times\:7}$

$\Rightarrow\: {\boxed{\sf{\green{r\:=\:105m}}}}$

• $\sf\underline\orange{Diameter\:=\:2r}$

$\to\:\sf\blue{Diameter\:=\:2\:\times\:105}$

$\to\:\sf\orange{Diameter\:=\:210m}$

$\to\:\sf\blue{2r\:=\:d\:=\: diagonal\:of\: square}$

$\star\:\underline{\boxed{\sf{\pink{Area\:of\: square\:=\:\dfrac{1}{2}\:(diagonal)^{2} }}}}$

$\mapsto\:\sf\purple{Area\:of\: square\:=\:\dfrac{1}{2}\:(210)^{2}}$

$\mapsto\:\sf\green{Area\:of\: square\:=\:\dfrac{\cancel{44100}^{22050}}{\cancel{2}_{1}}}$

$\mapsto\:{\large\underline{\boxed{\mathfrak{\red{Area\:of\: square\:=\:22050m^{2} }}}}}$

Answer 2

Answer:

Perimeter=660m

\Rightarrow\: \sf\purple{2\pi r\:=\:660}⇒2πr=660

\Rightarrow\: \sf\green{r\:=\:\dfrac{660}{2\pi}}⇒r=

2π

660

\Rightarrow\: \sf\purple{r\:=\:\dfrac{660\:\times\:7}{2\:\times\:22}}⇒r=

2×22

660×7

\Rightarrow\: \sf\purple{r\:=\:15\:\times\:7}⇒r=15×7

\Rightarrow\: {\boxed{\sf{\green{r\:=\:105m}}}}⇒

r=105m

\sf\underline\orange{Diameter\:=\:2r}

Diameter=2r

\to\:\sf\blue{Diameter\:=\:2\:\times\:105}→Diameter=2×105

\to\:\sf\orange{Diameter\:=\:210m}→Diameter=210m

\to\:\sf\blue{2r\:=\:d\:=\: diagonal\:of\: square}→2r=d=diagonalofsquare

\star\:\underline{\boxed{\sf{\pink{Area\:of\: square\:=\:\dfrac{1}{2}\:(diagonal)^{2} }}}}⋆

Areaofsquare=

2

1

(diagonal)

2

\mapsto\:\sf\purple{Area\:of\: square\:=\:\dfrac{1}{2}\:(210)^{2}}↦Areaofsquare=

2

1

(210)

2

\mapsto\:\sf\green{Area\:of\: square\:=\:\dfrac{\cancel{44100}^{22050}}{\cancel{2}_{1}}}↦Areaofsquare=

2

1

44100

22050

\mapsto\:{\large\underline{\boxed{\mathfrak{\red{Area\:of\: square\:=\:22050m^{2} }}}}}↦

Areaofsquare=22050m

2