Question

What is the area of the shaded region in the given circle in terms of pi and in simplest form?

Answer 1

@TheSmartOne @amistre64

Answer 2

the unshaded area can be found using

unshaded area = Area of the sector - area of the triangle

so the shaded area = area of the circle - unshaded area

Answer 3

you need the trig form of area of a triangle

\[A = \frac{1}{2} \times a \times b \times \sin(C)\]

the sector area is

\[A = \frac{60}{360} \times \pi \times r^2\]

hope it helps

Answer 4

area of the partial circle, plus area of the triangle ... would be my approach

Answer 5

the hardest thing might be in recalling how to find the area of the triagnle with the information given

Answer 6

i had left for a min.. but what would i Do, i know he gave me the formula but take me through it @amistre64

Answer 7

different appraoches but

we have part of a circles area, what proportion of the circle do we have?

Answer 8

the triangle has sides of 12 m and an angle 60 degrees

so

\[Area = \frac{1}{2} \times 12 \times 12 \times \sin(60)\]

the sector is

\[Area = \frac{60}{360} \times \pi \times 12^2\]

then the unshaded are = area of sector - area of triangle

Answer 9

last part is

Shaded = area of circle (radius 12) - unshaded area

Answer 10

amistre a full circle is 360 and they give us 60 so the other apart is 300 degrees? and campbell would I leave pi to the side??

Answer 11

yes 300 out of 360 is the proportion of the full circles area that is shaded

300/360

30/36

15/18 is a simplified ratio.

whats the area of a full circle of radius 12?

Answer 12

3.5/3.6

5/6 is even simpler :)

Answer 13

\[\frac56(\text{area of full circle})+(\text{area of triangle})=Area_{shade}\]

Answer 14

\[Area_{\triangle}=2\sqrt{3}\int_{0}^{6}x~dx\]

Answer 15

these are my options. What would i choose

Answer 16

im not choosing one for you, we can work the process and come to the solution. your full participation is required.

Answer 17

lol ok i respect that, 452.39 as the area if the radius was 12

Answer 18

lets keep it in pi

12^2 pi, our ratio is 5/6

12*12*5/6 pi is the area of interest to us

12*2*5 pi is what?

Answer 19

12*2=24*5=120

Answer 20

good, so we want 120 pi to start with

now the triangle we have a simple logical way, or the fomula way

Answer 21

logical way:

45 is less than 60, so its area is less



whats the area of this triangle?

Answer 22

if we use trapzoid area rule
\[A = \frac{base_1+base_2}{2}h\]
\[A = \frac{12+0}{2}*6\]

Answer 23

A=36

Answer 24

so teh area of a 60 degree angle triangle, is bigger than 36

what does this tell us?