Question

# Four equal circles are desc1ribed about the four comers of a square so that each eile
touches two of the others. Find the area of the space enclosed between the circumference
of the circles, each side of the square measuring 24 cm​

Answer 1

Answer:

 452.16 cm²       // 123.84 cm²    

Step-by-step explanation:

Note that: sum of diameters of 2 circles is equal to the length of the side of square.   Let the radii of the circles be r.

⇒ (diameter) + (diameter) = 24cm

⇒ (2r) + (2r) = 24 cm

⇒ r = 6 cm

Thus,

area of 1 circle = πr² = (22/7) 6²

                        = 113.04 cm²

Area of 4 such circles = 4*113.04

                         = 452.16 cm²

Area enclosed in circumference of circles

= area of circle  

= 4*113.04 = 452.16 cm²

If it is about the area enclosed between the circumference and square:

Area enclosed between the circumference  of the circles and square =

⇒ area of square - area of 4 circles

⇒ side² - 452.16

⇒ 24² - 452.16

⇒ 123.84 cm²

Answer 2

Answer Reffer to Attachment:-