Question

In a circular table cover of radius 32 cm, a
design is formed leaving an equilateral
triangle ABC in the middle as shown in
Fig. 12.24. Find the area of the design.
​

Answer 1

Step-by-step explanation:

Let ABC be the eq.land let o be the centre of the circle of r=32cm

Area of circle =rr^2

=(22/7x3232)cm2 =22528/7 cm2

Draw ABC

Now, /_ BOM= 1/2x120°=60° So, From ABOM,we have

OM/OB=cos 60°(1/2)

i.e., OM= 16 cm

Also, BM/OB= cos60°(1/2) i.e., BM= 16v3 cm

BC = 2 BM =32-13 cm Hence, area of ABOC = 1/2 BC.OM

=1/2x32 V3x16 area of ABC = 3x area of A BOC = 3x1/2x32 V3x16

= 76873 cm^2

Area of design= area of O - area of ABC = (22528/7 - 768V3)cm^2.