Question

A rectangle is 22 m long and 12 m wide. From its four corners quadrants of radius 2.5 m have been cut. Find the area of the remaining part.

Answer 1

Question :-

• A rectangle is 22 m long and 12 m wide. From its four corners quadrants of radius 2.5 m have been cut. Find the area of the remaining part.

$\bf\large \underbrace\red{Answer:}$

Given :-

• A rectangle is 22 m long and 12 m wide.
• From its four corners quadrants of radius 2.5 m have been cut.

To Find :-

• The area of the remaining part.

Formulas :-

$\bf \:\boxed{Area\:of\:Rectangle=l \times b}$

where,

• l = Length of rectangle
• b = Breadth of rectangle

${{ \boxed{\large{\bold{Area_{(Quadrant \: of \: Circle)}\:\ = \: \dfrac{1}{4} \pi r^2 }}}}} \:$

where,

• r = Radius of circle.

Solution :-

★ Step 1.

Length of rectangle = 22 m

Breadth of rectangle = 12 m

⇛ Area of rectangle = 22 × 12 = 264 m²

★ Step 2.

Radius of circle = 2.5 m

$\bf \:Area \: of \: quadrant = \dfrac{1}{4} \pi \: {r}^{2}$

$\bf\implies \:\dfrac{1}{4} \times \dfrac{22}{7} \times 2.5 \times 25$

$\bf\implies \:4.91 \: {m}^{2}$

Area of 4 quadrants = 4 × 4.91 = 19.64 m²

Now,

Remaining area = Area of rectangle - Area of 4 quadrants

⇛ Remaining Area = 264 - 19.64 = 244. 36 m²