Supposing we have a triangle where each of its edges comes from a section of a circle's edge, and that every corner is a right angle, I need to calculate the area and perimeter of it.

If the three circles that create this shape have radius one, one can show that their centers must be at $\sqrt2$ distance appart. But what is its area and perimeter? Thanks.

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    $\begingroup$ I suppose you have drawn a diagram. Divide the area into an ordinary triangle and three circular segments, and algebra the shit out of it. $\endgroup$ – hmakholm left over Monica Nov 7 '18 at 12:58

Here it is our right-angled Reuleaux triangle.

enter image description here

Assuming that the sides of the inner equilateral triangle have unit length, the blue arcs are arcs of circles with radius $\sqrt{3}$, associated to chords with unit length. It follows that the length of each arc is $\frac{\pi}{6}\sqrt{3}$. The enclosed area is the area of the equilateral triangle, $\frac{1}{4}\sqrt{3}$, plus three times the area of a circle segment, which can be seen as the difference between a circle sector with area $\frac{\pi}{4}$ and a triangle with area $\frac{abc}{4R}=\frac{3}{4}$.

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