Question

a circle have an area of 201 cm^2 is to be divided into two segments by a chord which 3 cm from the center of the circle. compute the area of the smaller segment.

Answer 1

With problems like these, a drawing is usually helpful to get you pointed in the right direction. See attached

The ultimate goal is to find the area of the blue region. To do this you'll first need to find the radius r. The formula needed here is

A = pi*r^2

The area of the circle is given to you. Use this and the formula to find r.

Once you know r, you'll use the value to find x (use the pythagorean theorem).

After figuring out what x is equal to, you can finally compute the area of the triangles. Also, you can use trig to figure out the angle \(\Large \theta\) which will help figure out the area of the sector

Then finally you can compute the area of the blue segment region

Area of blue region = (area of sector) - (area of triangles)

Answer 2

area of triangle = b*h/2
b = base
h = height


area of sector = (C/360)*pi*r^2
C = central angle
pi = 3.14 approximately
r = radius

btw a segment is what is shown in blue (see link below) and a sector is what is shown in green
http://www.differencebetween.info/sites/default/files/images/4/circle.jpg

Answer 3

also don't forget to double the value of theta to get the central angle

C = 2*theta

Answer 4

Thank you :)

Answer 5

@jim_thompson5910 should the area of the two triangles be equal to 22.25 cm^2 ?

Answer 6

let me check

Answer 7

The two triangles have combined area approximately equal to 22.24460797826

I used my calculator to compute pi. I didn't use pi = 3.14

If you do use pi = 3.14, then you get 22.2511718720957

Answer 8

I'd go with 22.24460797826 since it's more accurate. Unless your teacher wants you to use 3.14 for pi

Answer 9

hopefully that makes sense?

Answer 10

yeah thank you :). Should the answer be 53.65 cm^2 for the area of a segment?

Answer 11

This is what I got

area of 2 triangles = 22.24460797826
area of sector = 75.9021971297533


Area of blue region = (area of sector) - (area of triangles)
Area of blue region = (75.9021971297533) - (22.24460797826)
Area of blue region = 53.6575891514932

So it looks like you're very close. Again I'm using my calculator to store all the decimal digits (up to 15 digits I think?) to make it as accurate as possible. I'm sure your teacher is ok with a bit of error here and there.

Answer 12

Thank you so much for helping me @jim_thompson5910 :)

Answer 13

you're welcome