Area of quadrilateral knowing 3 sides and 2 angles

In summary, the conversation discusses finding the area of a quadrilateral when the lengths of three sides and two angles are known. The suggested method is to draw a picture and find the area of the bottom trapezoid and top triangle, then add them together. The individual also mentions using the cosine and sine formulas for triangles, but is unsure of how to start. They are given the lengths of 15, 12, and 2 and the angles of 120 degrees between 12 and 2 and 120 degrees between 15 and the unknown side.
  • #1
j9mom
31
0

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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  • #2
Draw a picture. Find the area of the bottom trapezoid and top triangle then add them.
 
  • #3
OK, let me try that. I never thought of a trapezoid. Thanks.
 

Related to Area of quadrilateral knowing 3 sides and 2 angles

What is the formula for finding the area of a quadrilateral when given 3 sides and 2 angles?

The formula for finding the area of a quadrilateral when given 3 sides and 2 angles is to first find the missing angle using the fact that the sum of the interior angles of a quadrilateral is 360 degrees. Once the missing angle is found, use the formula A = 1/2 * ab * sin(C) to calculate the area, where a and b are two of the given sides and C is the missing angle.

Can the area of a quadrilateral be found if only 2 sides and 2 angles are known?

No, the area of a quadrilateral cannot be found if only 2 sides and 2 angles are known. In order to calculate the area, at least 3 sides and 2 angles are needed. This is because a quadrilateral can have different combinations of side lengths and angles that result in the same area, making it impossible to find the exact area without sufficient information.

Is there a shortcut method for finding the area of a quadrilateral when given 3 sides and 2 angles?

Yes, there is a shortcut method for finding the area of a quadrilateral when given 3 sides and 2 angles. This method is known as the "side-angle-side" formula, which states that the area of a quadrilateral can be found by multiplying the three given sides and dividing by the sine of the angle opposite the third side.

What is the difference between the area of a quadrilateral and the perimeter?

The area of a quadrilateral is the measurement of the space inside the shape, while the perimeter is the measurement of the distance around the shape. Essentially, the area tells us how much space is enclosed by the shape, while the perimeter tells us the distance one would have to travel to go around the shape.

Can the area of a quadrilateral be negative?

No, the area of a quadrilateral cannot be negative. Area is always a positive value, representing the amount of space enclosed by a shape. If the calculated area is negative, it likely means that there was an error in the calculations or the given information was inaccurate.

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