A wall hanging is in the shape of a circle It has a triangle in it with each of - Maths - Areas Related to Circles

Question

A wall hanging is in the shape of a circle It has a triangle in
it with each of its vertex touching the circle, as shown in the
figure Also, the length of each of its sides is equal The diameter
of the wall hanging is 21 inches In the shaded portion, glossy
paper is to be pasted and the cost of glossy paper is Rs 25 per
square inches
and

What is the total cost of pasting the glossy paper?

priyanka saggu · Accepted Answer

Given diameter d = 21 inches so, r = 212 inchesarea of segment COB
= ar sector COB - ar ∆COBSector angle = θ =
120°Area of sector = πr2θ360
=227×212×212×120360 = 2312 = 115 5 in2∆OBD,
sin30 = ODOB12×212=ODOD = 214Similarly, cos 30 =32=
BDOB=2BD21BD = 2132Ar ∆COB = 12×BD×OD
=2132×12×214= 441163 = 47 738 in2
Area of segment COB = 115 5-47 738= 67 762 in2
â€‹Area of three such segment =
3×67 762â€‹=203 286 in2
Cost of pasting glossy paper at the rate Rs 25 per square inches=
25×203 286= Rs 5082 15