Question

A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A semi-circular portion with BC as diameter is cut off. Find the area of the remaining part.

Answer 1

Given: A rectangle ABCD with AB = 20 cm and BC = 14 cm. A semicircle with diameter BC is removed.

Step-wise calculation:

1. Area of rectangle

= AB × BC 

= 20 × 14

= 280 cm²

2. Diameter of semicircle = BC = 14 cm.

So, radius r = `14/2` = 7 cm.

3. Area of semicircle

= `1/2 xx π xx r^2` 

= `1/2 xx π xx 7^2`

= `1/2 xx π xx 49` 

= `(49π)/2` cm²

4. Area of remaining part

= Area of rectangle – Area of semicircle 

= `280 - (49π)/2` cm²

Numeric approximation (Use π = 3.14159265):

`(49π)/2 = 24.5π`

= 24.5 × 3.14159265 

= 76.9690

So, remaining area = 280 – 76.9690 = 203.0310 cm².

Exact area = `280 - (49π)/2` cm². 

Approximate area = 203.03 cm².