What is the area between four circles with a radius of 10?

This is assuming that the four circles are arranged in a square, with each circle touching two other circles at their tangents.

First, you need to determine the area created by drawing a square between the center points of all of the circles.

Circle radius = 10
Side of square = 10 * 2, or 20
Area of square = 20 * 20, or 400

Now that you have that area, you can deduct the four quarters of the circles inside the square area. You can do it the long way, but four quarters of identical circles equals the area of one of the circles

Area of circle = pi * r^2

= pi * 100
=3.14159 *100
=314.159

Square Area - (4) quarter circle area

400 - 314.159
= 85.841