Question

Four equal circles, each of radius 5 cm touch each other as shown in fig. Find the area included etween them.

Answer 1

Area required shaded = (area of square ABCD) – (Area of 4 quadrant)

Side of square = 5cm + 5cm

= 10cm

Area of square = side × side

= 10𝑐𝑚 × 10𝑐𝑚 = 100𝑐𝑚²

Area of quadrant =`1/4` (𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒 𝑤𝑖𝑡ℎ 𝑟𝑎𝑑𝑖𝑢𝑠 5 𝑐𝑚)

=`1/4×pir^2`

=`1/4×22/7× 5 × 5 = (25 × 3.14) 1/4 cm^2`

Area included between circles = (area of square) – 4(area of quadrant)

= `100  – (1/4× 25 × 2.14)`

= 100 – 78.5

= 21.5cm²