Find area of a 'curved triangle'
Originally, there was a pen of radius 10cm for her animals to safely roam around in (Figure 1).
She found that the animals often destroyed the vegetation on the floor before it could regrow. She decided to split the pen into 3 equal lengths of AB, BC and CD (Figure 2).
She found she could join them together to create an equilateral triangle that had a side length of 10cm within the 'curved triangle'. (Figure 3).
1) What is the area of the whole 'curved triangle'?
2) She found she could enclose it in a square, with the sides of the curved triangle just touching the sides of the square. She found that any square she drew around this curved triangle was the same size. Assuming this is true, what is the side length of the square?