Question

ABCD is a square paper of side 14 cm. If a quadrant with B as centre is cut off, find the area of the remaining paper.

Answer 1

Given:

• ABCD is a square paper of side 14 cm.
• A quadrant with centre at B is cut off.

Step-wise calculation:

1. Area of square ABCD:

`"Area"_("square") = "side"^2`

= 14 × 14

= 196 cm²

2. Radius of the quadrant is equal to the side of the square 14 cm, since B is a vertex of the square.

3. Area of the quadrant one-fourth of a circle: 

`"Area"_("quadrant") = (πr^2)/4`

= `22/7 xx (14 xx 14)/4`

= `22/7 xx 196/4`

= `22/7 xx 49`

= 154 cm²

4. Area of the remaining paper after cutting the quadrant:

Remaining Area = Area square – Area quadrant

= 196 – 154

= 42 cm²

The area of the remaining paper after cutting off the quadrant with center B is 42 cm².