Question

Find the area of the shaded region in the figure. (Round your answer to one decimal place.) α = π/3, b = 12

Answer 1

non shaded area = area of segment - area of triangle

shaded area = total area - non shaded area

equation for area of segment = ...?
and equation for area of triangle = ...? @iiagho ?

Answer 2

EQN for area of segment = 1/2 x r^2 x (theta - sin theta) as ur angle is in radians

u can work out area of triangle and solve, yeah?

Answer 3

pi/3 means equilateral triangle , all sides = 12 therfore area = \[\sqrt{3}/4 \times 12^{2}\]

Answer 4

=root3 * 144/4 = root3 * 36 = 62.3

Answer 5

AREA OF TRIANGLE = 1/2 base * ht
1st:
ht from h^2 = a^2 + b^2
12^2 = ht ^2 + 6^2
ht^2 = 144-36
ht = sqrt 108
ht = 10.3923

2nd:
Area = 1/2 base * ht
= 1/2 * 12 * 10.3923
= 62.354

AREA OF SECTOR = (angle/2) * r^2
= (pi/3)/2 * 12^2
= (pi/6) * 144
= 75.398


AREA OF SEGMENT = area of sector - area of triangle
or
= 1/2 x r^2 x (angle - sin angle)
= 1/2 * 12^2 * (pi/3 - sin pi/3)
= 13.044


AREA OF CIRCLE = pi r^2
= pi * 12^2
= 452.38

Are you ok from here to find SHADED AREA? @isiagho ??