Question

Find the area of the shaded region. Leave your answer in terms of and in simplest radical form.

Answer 1

hey saif isnt that an equilateral triangle?

Answer 2

Yess boss it is.

Answer 3

for my first my first attempt on this qn i think we should find area of the triangle , area of the sector and area of the circle separately ...let me see if there is a simpler method

Answer 4

there are two main methods.

Answer 5

@saifoo.khan which is the other way?

Answer 6

Find the rest circle + triangle that's easy.

second way. find the whole circle, subtract the white part.

Answer 7

can you guys solve and explain please?

Answer 8

area of a circle is A=(pi)r^2 notice in this case we know r = 12 so therefore our area of a circle is A=144pi

Answer 9

now we need to subtract this by that white part which iss

Answer 10

@saifoo.khan use first way is easier

Answer 11

@.Sam. , agree.

Answer 12

We can use simple P1 math to solve by second method too. ;)

Answer 13

there are 6 sectors
6 times 60 =360 degree
so, we dont use 6 sectors but 5,
then ,
5 sectors + triangle = shaded area

Answer 14

@.Sam. , check this out:
http://openstudy.com/updates/4fced71be4b0c6963ad9ed4b

Answer 15

@saifoo.khan i think we nned area of sector too

Answer 16

\[\text{Sector}~A=\frac{1}{2}r^2 \theta\]

Answer 17

That will give you perfect answer. no worries. :)

Answer 18

yep

Answer 19

5 sectors + triangle = shaded area
\[5(\frac{1}{2}(12)^2(\frac{\pi}{3}))+\text{Area of \triangle}\]

Answer 20

area of a circle is A=144pi
\[area of unshadeed part = r ^{2}[\pi \theta/360^{0} - \sin \theta/2]\]
=144{[22/7*60/360 ] - [(sqrt 3/2)/2]}
area of circle - area unshaded is =area of shaded part

Answer 21

120 pi - 26sqrt3

Answer 22

so which one is it?
(120+ 6 sqrt 3)m²
(142+ 36sqrt 3)m²
(120+ 36 sqrt 3)m²

Answer 23

sorry 120 pi -36sqrt3

Answer 24

you mean + not -?