Area of quadrilateral knowing 3 sides and 2 angles

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SUMMARY

The discussion focuses on calculating the area of a quadrilateral given three side lengths (15, 12, and 2) and two angles (both 120 degrees). The user seeks an equation to find the area and the measurements of the remaining angles. A suggested approach involves dividing the quadrilateral into a trapezoid and a triangle, utilizing known trigonometric formulas to derive the area. This method effectively simplifies the problem and provides a clear pathway to the solution.

PREREQUISITES
  • Understanding of basic trigonometric functions (sine and cosine)
  • Familiarity with the properties of quadrilaterals
  • Knowledge of area calculation for trapezoids and triangles
  • Ability to apply the Law of Cosines for angle calculations
NEXT STEPS
  • Study the Law of Cosines to find unknown angles in quadrilaterals
  • Learn how to calculate the area of trapezoids using side lengths and angles
  • Explore methods for decomposing complex shapes into simpler geometric figures
  • Practice solving problems involving quadrilaterals with known sides and angles
USEFUL FOR

Students studying geometry, mathematics educators, and anyone interested in solving problems related to quadrilaterals and trigonometry.

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Homework Statement


Is there an equation in which I can find the area of a quadrilateral when I know the length of three of the sides and 2 of the angles? Also I really need to find the measurement of the other two angles.


Homework Equations

I know the cos and sin formulas of triangles, and may be I can use that but I do not know how to start

The lengths I know are 15, 12 & 2 and the angles I know are 120 degrees between the 12 and 2 and 120 degrees between the 15 and the side I don't know.



The Attempt at a Solution



I really need a nudge to start.. this is a small portion of a much bigger problem.
 
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Draw a picture. Find the area of the bottom trapezoid and top triangle then add them.
 
OK, let me try that. I never thought of a trapezoid. Thanks.
 

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