Question

In the given figure ABCD is a square tile, on which rangoli design is drawn.
Find the area of the rangoli design and the area of the remaining part of the tile
ABCD, if AB = 20m, PQ = 8m, OQ =5m and OP= 9 m

Answer 1

o is center of whole rangoli.

In Rhombus ABCD ,

AO=OP+PA=2+2=4 units.

And, OB=OQ+QB=2+1=3 units.

Now,

We know that the diagonals of the rhombus bisect at 90

0

∴ In ΔOAB ,

AB

2

=OA

2

+OB

2

⇒AB

2

=4

2

+3

2

⇒AB

2

=

25

⇒AB=5 units.

Which is diameter of semicircle

So, radius of semicircle is

2

5

=2.5 unit