OMG PLEASE HELP The diagram shows three circles with radii r=10 cm. The centers also form the vertices of an equilateral triangle.

 16.205 cm²

It takes some time, but it's not impossible!

Step-by-step explanation:

Find the area of the triangle, then subtract the area of the three sectors.

 The three sectors are each 60° so they add to 180° which is equivalent to half the area of one circle.  

The area of the triangle is one half base times height. To find the height of the triangle, use the Pythagorean Theorem to get the length of the perpendicular bisector.

a² + b² = c² .  

C is the side length, 20cm. (the length of two radii) B is half the side length 10cm. A is the "altitude" or height we need to find.  

a² + 10² = 20²

a² + 100 = 400 .  a² = 400-100

a² = 300

a = √300   a ≈ 17.3205

Area of triangle: A= bh/2

A = (20 × 173.205)/2

Triangle Total Area ≈ 173.205

To the area of the circle, use the equation A = πr²  

A = 3.14 × 10²

A = 3.14 × 100  

Circle Total Area =  314 cm².  

You could take 1/6 of that, and then multiply by 3,  or just take half

Area of sectors=  157 cm²

Triangle Area - Sectors Area = Blue shape Area

173.205 - 157 ≈ 16.205 cm²

Hi, are you still active?