Question

$\huge \red \mid\fbox\red{Question:-}\red\mid$

□ ABCD is a rectangle. l(AB) = 24 cm, l(BC) = 18 cm. A sector of radius 7 cm is cut off at each corner of the rectangle. What is the area of the remaining figure? ​

Answer 1

We have -

Firstly we have a rectangle ABCD with,

➝ Length = 24cm

➝ Breadth = 18cm

⠀

And we have four sectors with

➝ Radius = 7cm

⠀

It is given that a sector is cut off at each corner of the rectangle. Since, four sectors make a circle.

So, we have

• A circle
• A rectangle

⠀

Finding area of rectangle ABCD

$\large{\bf{\longmapsto{\boxed{\pink{Area = Length \times Breadth}}}}}$

⠀

$\tt\dashrightarrow{Area_1 = 24 \times 18}$

$\bf\dashrightarrow{Area_1 = 432\: cm^2}$

⠀

Finding area of circle

$\large{\bf{\longmapsto{\boxed{\pink{Area = \pi r^2}}}}}$

⠀

$\tt\dashrightarrow{Area_2 = \dfrac{22}{7} \times (7)^2}$

⠀

$\tt\dashrightarrow{Area_2 = \dfrac{22}{7} \times 49}$

⠀

$\tt\dashrightarrow{Area_2 = 22 \times 7}$

⠀

$\bf\dashrightarrow{Area_2 = 154}$

⠀

Now, we have

➝ Area of rectangle = 432cm²

➝ Area of circle = 154cm²

⠀

For finding the area of remaining part, we subtract the area of circle from the area of rectangle.

⠀⠀⠀⠀⠀⠀⠀⠀$\boxed{\bf{\red{Area_1 - Area_2}}}$

⠀

➝ Required area = 432 - 154

➝ Required area = 278 cm²

⠀

★ $\small\underline{\sf{Thus,\: area\: of\: remaining\: part\: is\: 278cm^2.}}$