MHB What is the area of the quadrilateral?

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The quadrilateral KLMN is inscribed in a circle with center O, where KL measures 18 and LM measures 24, with KN equal to NM. The area of triangle KLM is calculated as 216, while triangle KNM, being isosceles with base KM as 30 and height ON as 15, has an area of 225. The total area of quadrilateral KLMN is thus the sum of the areas of both triangles, which equals 441. The use of the Pythagorean theorem and properties of inscribed angles were key in determining these areas. The discussion highlights the geometric relationships within the quadrilateral and the circle.
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https://gyazo.com/55afe69c0f00bff85a3a9c53bd353b42

Sorry for the really poorly drawn and lit picture...

Basically this quadrilateral is drawn inside a circle whose middle point is O. Here is the info I was given

KL = 18
LM = 24
KN = NM

What I need to find out is the area of KLMN.

What I did there split the quadrilateral into 2 with a diameter. I found out the length of that with the pythagorean theorem. It was 30. So logically the area of that triangle is 24x18/2 = 225.

But how do I find out the volume of the second triangle? I know it's really simple but I just can't figure it out...
 

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If KM is a diameter, then triangle KNM is isosceles with base KM = 30 and height ON = 15 $\implies$ area of triangle KNM is 225.

triangle KLM is inscribed in a semicircle, therefore angle L is 90 degrees ...

area of triangle KLM is 216
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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