Q32 of 37 Page 13

It is proposed to add to a square lawn with the side 58m, two circular ends (the centre of each circle being the point of intersection of the diagonals of the square.) Find the area of the whole lawn [Take π=3.14]


ABCD is a square lawn of side 58m. AED and BFC are two circular ends.


Now, diagonal of the lawn = √(58)2 + (58)2 = 58√2m


It is given that diagonal of square = Diameter of circle


∴The radius of a circle having a centre at the point of intersection of diagonal



It is given that square ABCD is inscribed by the circle with centre O.


∴Area of 4 segments = Area of circle – Area of square


= πr2 – (side)2






m2



= 961.14m2


Area of whole lawn = Area of circle – Area of two segments



=5286.28 – 961.14


= 4325.14 m2


More from this chapter

All 37 →
30

In the given figure ABCD is a square whose each side is 14cm. APD and BPC are semicircles. Find the area of the shaded region.

 31

In the given figure a square OABC is inscribed in a quadrant OPBQ. If OA =20cm, find the area of the shaded region.

 33

Find the difference between the area of a regular hexagonal plot each of whose side is 72 m and the area of the circular swimming tank inscribed in it.

34

In the figure, ABC is a quadrant of a circle of radius 14cm, and a semicircle is drawn with BC as diameter. Find the area of the shaded region.