Two overlapping arcs in a square

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Question from Jean, a teacher:

I have a square with side 4 cm. There are two overlapping arcs going from vertex to diagonal vertex. The other two vertices are the center of the arcs, which are shaded. How do I find the area of the shaded arcs? The overlapping arcs when shaded resemble a long thin football
Thank you for your help.

We have two responses for you

Hi Jean,

square

In my diagram which is part of what you described, the red region is one-quarter of a circle of radius 4 cm. What is its area? What is the area of the green region?

Penny

Consider the figure below:

square

One can calculate the two parts of the region each as the difference between a sector of the circle and the area of the triangle.

Walter

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