A rectangular piece is 20 m long and 15 m wide.

Question:

A rectangular piece is 20 m long and 15 m wide. From its four corners, quadrants of radii 3.5 m have been cut. Find the area of the remaining part.

Solution:

It is given that, the quadrants of radius r have been cut from the four corners of a rectangular piece is of length and width.

We have to find the area of remaining part.

We know that,

Area of rectangle $=I \times w$

$=20 \times 15$

 

$=300 \mathrm{~m}^{2}$

Area of quadrant $=\frac{1}{4} \pi r^{2}$

$=\frac{1}{4} \times \frac{22}{7} \times 3.5 \times 3.5$

$=9.625 \mathrm{~m}^{2}$

Now,

Area of remaining part $=$ Area of rectangle $-4 \times$ Area of quadrant

$=300-4 \times 9.625$

 

$=300-38.5$

$=261.5 \mathrm{~m}^{2}$

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