Question

32.
Find the area of the shaded region in the triangle PQR where radius of
each sector drawn at the vertex of the triangle is 7cm.​

Answer 1

Step-by-step explanation:

PQR is an equilateral triangle

angle P = angle Q = angle r = 60°

AREA OF SHADED REGION = AREA OF TRIANGLE - AREA OF 3 SECTORS

area of triangle = 1/2 *sin60*r^2

= 1/2 * root3/2 *( 7 )^2

= 1/2 * 1.73/2 * 49

= 1/2 * 0.865*49

= 1/2 *42.385

= 21.1925 cm^2

Thieta = 60°(equilateral triangle)

area of 3 sectors = 3*thieta/360 * pie (r)^2

= 3*60/360*22/7*49

= 3*1/6*22*7

= 3*1/6*154

= 462/6

= 77 cm^2

21.19525cm^2 - 77cm^2 =