Question

WILL MEDAL

Find the area of the shaded segment. Round your answer to the nearest square meter.

'https://s32.postimg.org/j10izuso1/14676563234138.png'

What i've tried to do so far is this:

A= 60/360 x (3.14)(6)^2 but that doesn't give me what I want. Im at a loss, any help would be appreciated!

Answer 1

so - what can you tell about the triangle below the shaded segment?

2 sides are equal and the angle between them is 60 deg?

Answer 2

Correct

Answer 3

so - what can YOU tell about the triangle below the shaded segment?

Answer 4

All sides are equal?

Answer 5

yes - it is 'equilateral'

Now the equation you wrote above (1/6 pi r^2) is the area of the SECTOR (i.e. the total 'pie slice' piece)

so you need to work out the area of the triangle and subtract it from the are of the sector

Answer 6

so the sector is including the shaded area as well?

Answer 7

How would I set up an equation to get the triangle?

Answer 8

the sector is the whole pie slice

the segment is what oyu want to find

so subtract the triangle area.

You can find out the area of the triangle for yourself (3 sides - use 'herons formula)
or work out the height from the side and angles

Answer 9

I'm not familiar with heron's formula at all. So what exactly would i change/add to my equation to just get the triangle?

Answer 10

?

Answer 11

Heron's wouldn't be the most efficient way of solving this problem but just a btw:
Heron's formula is a handy formula that finds the area of any triangle given its lenghts.
Given side lengths a,b,c, let s(semi-perimeter) be (a+b+c)/2.
The area of the triangle is then \[\sqrt{s(s-a)(s-b)(s-c)}\]

Answer 12

Im still really confused...

Answer 13

on Heron's or...

Answer 14

Now you have a right triangle.
You can use trig or the Pythagorean theorem to find h, the height of the triangle.

Answer 15

as I said
"You can find out the area of the triangle for yourself (3 sides - use 'herons formula)
or work out the height from the side and angles"

Answer 16

https://en.wikipedia.org/wiki/Circular_segment