What’s the area?

Transcript

draw three mutually tangent unit circles like this these three circles enclose an area as shown here can you determine the area of the enclosed shape pause the video and think about it before I show you an answer one way to answer this problem is to realize that the centers of the three circles can be connected to form an equilateral triangle with a side length of two this has an area ofare < TK of three but then this equilateral triangle can be decomposed into these three wedge shaped pieces in the area we want each of the wed shaped pieces has an area ofk 6 so the area we want is the 6 which simplifies to the < of 3 - pi/ 2 let me know in the comments if you solved it a different way