Find the area of the shaded portion in the equilateral triangle with sides 6.

First, let's get the area of the entire triangle since we'll need it later. The area of a triangle is A=1/2*b*h

We can find the height with the Pythagorean theorem by splitting the triangle in half. 
3^2+b^2=6^2
9+b^2=36
b^2=27
b=√27

Then we can find the area:
A=1/2*6*√27
A=3√27   or   =9√3   or 15.59

Now we can find the area of each region in the triangle other than the shaded region because they are all portions of a circle.

Each region has an angle of 60 because this is an equilateral triangle. Therefore the area of each region other than the shaded region will be 1/6 the area of a circle with a radius of 3 because a full circle is 360 degrees.
A=pi*r^2/6
A=pi*9/6
A=4.71

So three of these regions would have an area of 14.14

We do the area of the triangle minus the area of these regions to get the area of the shaded region
15.59-14.14 = 1.45

Hope this helps!

9√3 - 4.5π

Step-by-step explanation:

The first step here is to find the area of the whole figure. Then, we can subtract the areas of the non-shaded parts to end up with the area of shaded parts. The sides of this equilateral triangle are 6.

The formula for an equilateral triangle is: 1/4(s^2) sqrt3

1/4 (6^2) sqrt3

1/4 (36) sqrt3

9sqrt3

Sector Formula: a = measure of arc/360 πr^2

Measure of arc is 60 degrees, since the angle is 60, as equilateral triangles have all 3 angles as 60 degrees. Since the arc is equal to the angle, it is also 60 degrees.

60/360 πr^2

1/6π (3^2)

1/6π (9)

9/6π

Now, we multiply this by 3.

9/6π x 3 =

4.5π

AREA OF SEGMENT: 9sqrt3 - 4.5π