Question

Find the area of the shaded portion intersecting between the two circles.

help me i dnt have enough time to get this work done before scool starts so HELP ME!!

click pic below

Answer 1

i cant see a pic

Answer 2

same here!

Answer 3

and they gave you no numbers to work with?

Answer 4

is in the diagram

Answer 5

This is taking a 60 degree arc area and subtracting the area of an equilateral triangle. We have 2 of these so it's that value times 2.
This is 1/6 of a circle area so:
\[ \frac{1}{6} \pi (4)^{2} = \frac{8}{3} \pi \]
The triangle area is \[\frac{1}{2} base*height\]
The height is calculated using pythagoreans. We have a hypotenuse of 4 and a side of 2 so the height is:
\[4^{2} - 2^{2} = 16-4 = 12 = 2 \sqrt{3}\]
The base of the triangle is 4. The height is 2 sqrt 3. So the area is:
\[\frac{1}{2}(4)(2\sqrt{3})=4\sqrt{3}\]
The area of the sliver is:
\[\frac{8}{3}\pi-2\sqrt{3}\]
We have two of these slivers of circle so we will be multiplying the area by 2:
\[2(\frac{8}{3}\pi-2\sqrt{3}=\frac{16}{3}\pi-4\sqrt{3}\]