# Mensuration-30

### From Homeworkwiki

**A rectangle with length and breadth 12 cm and 5 cm is drawn within a circle. Find the area of the remaining space outside the rectangle **

**Solution:** Length of the rectangle = 12 cm

Width of the rectangle = 5 cm

The diagonal of the rectangle passes through the center of the circle.

The diagonal = √(Length^{2} + Breadth^{2}) = √(12^{2} + 5^{2})

= √(144 + 25) = √169 = 13 cm

Therefore, Diameter of the circle = 13 cm

=> Radius of the circle = 13 / 2 cm = 6.5 cm

Area of the circle = Π r^{2} = 3.14 x (6.5)^{2} cm^{2} = 132.665 cm^{2}

Area of the remaining space outside the rectangle = Area of the circle - Area of the rectangle

= (132.665 - 60) cm^{2} = 72.665 cm^{2} = 72.67 cm^{2} (correct to two decimal places)