Question

Find the area of the shaded portion in the equilateral triangle with sides 6.
(assuming the central point of each arc is its corresponding vertex

Answer 1

Diagram

Answer 2

First find the area of the triangle, ( i don't know if you learnt this)
To find area of an equilateral triangle, use the following formula
Area= 3a^2 / 4sqrt(3) where a is the length of one side.

Area = 3(6^2) / 4sqrt(3)
= 27/ 4 sqrt(3)
= 15.6

Note that each corner is 60degrees since it is an equilateral triangle. meaning that arc is actually 60/360 = 1/6 of a circle.

3 1/6 of a circle make up a semicircle. This means that all the white area in the triangle adds up to a semicircle with a radius of 3.

Area of semicircle = 0.5 pi r^2
=0.5 pi 3^2
=4.5pi

Area of shaded region = area of triangle - area of semicircle = 15.6 - 4.5pi= 1.45

Answer 3

Geometry hard, but I think I got it.

Answer 4

keypoint is to note that the unshaded parts actually are part of a circle.

Answer 5

I see it now the arch.

Answer 6

What about this problem? No diagram provides none.
Express answer in exact form.
Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius. (Hint: A chord divides a circle into two segments. In problem 1, you found the area of the smaller segment.)
Click once to select an item at the bottom of the problem.
Click again to drop the item in its correct place

Answer 7

Hmm im having problems with that cause i have no idea why a chord divide a circle into 2 segments.

One chord would only produce one segment, how did they get 2.

Answer 8

The first question I asked can you put in this in this form?\[A=_\sqrt{?}-_/_\pi\]

Answer 9

In exact form it would be \[\frac{27}{4\sqrt{3}} - \frac{9}{2}\pi\]

Answer 10

answer was right. what about the second question?

Answer 11

@yukiwolf I'm going to post a new question with other problems and I'll send you a link.

Answer 12

im here

Answer 13

Hers the Link to the new question. http://openstudy.com/study#/updates/4fe35dbbe4b06e92b8722283