math help please (algebra i think)

[Corporate Thug]

my little cousin has this math problem and although it is really easy, i havent taken a math class in years and i have no clue how to solve it.

look at this pic:

circles.GIF

assuming all the circles have a radius of 10 cm (i know the picture doesnt look like it ), what is the area of the black region

thank in advance

 

Uh, that's not algebra. That's kinda tough!

 

[Corporate Thug]

yeah, i dont really know what it is...

 

[JohnCU]

I'm in Calculus 2 and I still have no idea how you'd do that...

 

[notfred]

It's a triangle 20cm on a side. Find the area of that. Then find the area of each circle. The triangle takes up a 60 degree arc of each circle. That's 1/6 of a circle. subtract 1/6 of each circle's area from the overall area of the triangle.

 

[JetBlack69]

You could draw a triange by connecting the centers of the three circles. Then, you could find the area of the triangle and subtract the pieces of circles (which are just a percentage of the total area of the circle, based on degrees) from the triangle.

At least that's how I would go about it.

EDIT.
Yep, notfred beat me to it.

 

[Corporate Thug]

thanx guys, i finally figured it out

 

[Amorphus]

Ugh, the perspective really screwed me up.

 

[DrPizza]

Originally posted by: JohnCU
I'm in Calculus 2 and I still have no idea how you'd do that...

no offense meant, but...
pathetic

The hard way to do it would be to write an equation for each circle and integrate to find the area between the curves (if you're in calc II). But, even someone in calc II should be able to handle that.

I'll agree it's a fairly involved problem, but not past the geometry level.