What is the area of the quadrilateral?

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In summary, the conversation discusses finding the area of the quadrilateral KLMN, which is drawn inside a circle with center O. The area of triangle KNM is 225 and the area of triangle KLM is 216. The method used to find the area of KLMN involves splitting it into two triangles using a diameter and using the Pythagorean theorem to find the length.
  • #1
Monokonos
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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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  • #2
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
 

1. What is a quadrilateral?

A quadrilateral is a two-dimensional shape with four straight sides and four angles. Examples of quadrilaterals include squares, rectangles, trapezoids, and parallelograms.

2. How do you find the area of a quadrilateral?

To find the area of a quadrilateral, you can use the formula A = (1/2)bh, where A is the area, b is the length of the base, and h is the height of the quadrilateral. If the quadrilateral is irregular, you can also divide it into smaller shapes and find the area of each shape, then add them together.

3. What are the different methods for finding the area of a quadrilateral?

There are several methods for finding the area of a quadrilateral, including using the formula A = (1/2)bh, dividing it into smaller shapes, using the Pythagorean theorem, or using the shoelace formula. The method you choose will depend on the given information and the type of quadrilateral.

4. Can you find the area of a quadrilateral if you only know the lengths of its sides?

Yes, you can find the area of a quadrilateral if you know the lengths of its sides. You can use the Heron's formula, which is A = √(s(s-a)(s-b)(s-c)(s-d)), where A is the area and s is the semi-perimeter (half of the perimeter) of the quadrilateral. Alternatively, you can divide the quadrilateral into smaller shapes and use the formula for finding the area of each shape.

5. Is it possible to find the area of a quadrilateral without knowing all of its angles?

Yes, it is possible to find the area of a quadrilateral without knowing all of its angles. You can use the formula A = (1/2)bh, where b is the length of the base and h is the height of the quadrilateral. If the quadrilateral is irregular, you can also divide it into smaller shapes and find the area of each shape, then add them together.

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