What is the area of the quadrilateral?

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SUMMARY

The area of the quadrilateral KLMN, inscribed in a circle with center O, is calculated by dividing it into two triangles: KLM and KNM. The lengths provided are KL = 18 and LM = 24, leading to the area of triangle KLM being 216 square units. The diameter KM measures 30 units, making triangle KNM isosceles with an area of 225 square units. Therefore, the total area of quadrilateral KLMN is 441 square units.

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View attachment 7882
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
 

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