Question 1166972
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            The description in the post is not clear enough to identify the areas of the interest by a unique way.


            I will interpret the post as  " to find the sum of the areas of the two lunes ".


            For the meaning of the term  " lune "  in  Geometry  see this  Wikipedia article

            https://en.wikipedia.org/wiki/Lune_(geometry)



<U>Solution</U>


<pre>
The diameter is  d = {{{sqrt(20^2 + 21^2)}}}   (Pythagoras),  or

    d^2 = 20^2 + 21^2 = 841.



The area of the large upper-right semi-circle is therefore  

    {{{(1/2)*pi*(d^2/4)}}} = {{{pi*(841/8)}}} = {{{105.125*pi}}}.


From it, subtract the area of the right angled triangle with the legs 20 and 21; this area is {{{(1/2)*20*21)}}} = 210.


You will get the sum of areas of two segments of the large circle

    segments_area = {{{105.125*pi-210)}}}.               (1)



The area of two smaller semi-circles is  

    {{{(1/2)*pi*(20^2/4) + (1/2)*pi*(21^2/4)}}} = {{{105.125*pi}}}     (2)

( ! same as the area of the large semi-circle !)



Finally, to find the area under the problem's question, you should subtract the area of two segments  (1)  
from the area of two small semicircles  {{{105.125*pi}}} of (2).


You will get then the answer to the problem's question as  210 square units.
</pre>

Solved.