In a circular table cover of radius 12 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in figure. Find the area of the design. [4 MARKS]
Concept: 1 Mark
Application: 3 Marks
Each side of the equilateral triangle subtends 120∘ at the centre.
The area of the each sector =120360×π×122=150.72 cm2
Perpendicular from chord is drawn to the centre. By RHS congruence, the two triangles will be congruent.
The perpendicular divides the chord into equal halves.
The angle subtended by each triangle at the centre is 60∘.
Height of perpendicular =rcos 60∘=12×0.5=6 cm.
Length of chord =2×r×sin 60∘=24×√(3)2=20.6 cm
The area of each small triangle =0.5×20.6×6=61.8 cm2
The area of each segment =150.72−61.8=88.92 cm2
The total area is =88.92×3=266.76 cm2
The area of circle =π×122=452.16 cm2