SOLUTION: PQR is a triangle right angled at P. The lengths of the sides PQ, QR and PR are rcm p cm and q cm, respectively. Semi-circles are drawn on each side of the triangle. Show that the

Question 773501: PQR is a triangle right angled at P. The lengths of the sides PQ, QR and PR are rcm p cm and q cm, respectively. Semi-circles are drawn on each side of the triangle. Show that the sum of the areas of the semi - circles, A, can be expressed as A = 1/4 π * p^2
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I can only draw full circle. I cannot draw semicircles, so pretend you do not see the wromg half of the circles.
According to Pythagoras, .
The area of a circle is

so the area of a smicircle is
The circles' diameters are , and , so their radii are , and .
Then the areas of the semicircles are
, and .
The sum of the areas of the semicircles is

Substituting for , we get
sum of semicircle areas =
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