See below for the proof that the areas of the lune and the isosceles triangle are equal
<h3>How to prove the areas?</h3>
The area of the isosceles triangle is:

Where r represents the radius.
From the figure, we have:

So, the equation becomes

Evaluate

Next, we calculate the length (L) of the chord as follows:

Multiply both sides by r

Multiply by 2

This gives


The area of the semicircle is then calculated as:

This gives

Evaluate the square

Divide

Next, calculate the area of the chord using

Recall that:

Convert to radians

So, we have:

This gives

The area of the lune is then calculated as:

This gives

Expand

Evaluate the difference

Recall that the area of the isosceles triangle is

By comparison, we have:

This means that the areas of the lune and the isosceles triangle are equal
Read more about areas at:
brainly.com/question/27683633
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