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Srinivas
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How to find the area of this irregular quadrilateral?
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In summary, the conversation discusses the difficulty in finding the area of an irregular quadrilateral using only the lengths of its sides. The suggested method is to divide the quadrilateral into triangles and use Heron's formula, but this requires knowledge of at least one angle. Another formula, Bretschneider's formula, can be used but also requires knowledge of two opposite angles. The possibility of the given dimensions being measured on a sphere is also mentioned. Ultimately, it is determined that there is not enough information to solve the problem with just the side lengths.
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How irregular is this? The picture makes it look like a right trapezoid, which has a known formula.Srinivas said:
There may be a way to get the area of a quadrilateral using only the sides (like Heron's formula for triangles) but the only process I'm sure of requires knowledge of one of the angles as well. The usual method for finding the area of an irregular figure is to break it into triangles and find the sum of the areas of the triangles. If you have the angle of just one of these triangles you can find the length of the diagonal and can use Heron's formula to find the area of the triangle. Then you can get the other two angles and work from there.
-Dan
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Srinivas
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Two right angles.topsquark said:
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Srinivas
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Dan, two right angles are there in the image.
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Okay, so this is not an irregular quadrilateral, it's a right trapezoid. The area for a trapezoid is $A = \dfrac{1}{2} (b_1 + b_2) h$. What can you use for the bases and the height?Srinivas said:
-Dan
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Mark44
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It wasn't clear from the drawing that the angles at the base were right angles.Srinivas said:
In any case, if you have an irregular quadrilateral you can find its area using Bretschneider's Formula - https://en.wikipedia.org/wiki/Bretschneider's_formula. However, in addition to the lengths of the four sides, you also need to know the measures of two opposite angles.
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OmCheeto
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I think the first thing to do in this problem would be to determine if such a figure can be created with two right angles with the given dimensions.
243 ≠ 265
Perhaps the lengths were measured on a sphere?
243 ≠ 265
Perhaps the lengths were measured on a sphere?
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Do you have the lengths of the diagonals?
(That is to say, do you know all of the distances between all of the corners?)
https://en.wikipedia.org/wiki/Cayley–Menger_determinant#Set_Classifications
https://terrytao.wordpress.com/2019...nger-determinant-and-the-radius-of-the-earth/
(That is to say, do you know all of the distances between all of the corners?)
https://en.wikipedia.org/wiki/Cayley–Menger_determinant#Set_Classifications
https://terrytao.wordpress.com/2019...nger-determinant-and-the-radius-of-the-earth/
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Theia
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If I'm not mistaken, the quadrilateral in the picture cannot exist. Could you double check the numerical values of the problem, please? Just to make sure, we're talking about the right problem.Srinivas said:
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pasmith
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I think you don't have enough information to solve the problem from just the side lengths.
You can decompose the figure into two triangles. However, all you know about each triangle are the lengths of two of its sides. You need an additional piece of information - either the length of the third side (ie one of the diaongals of the quadrilateral) or an angle - in order to solve those triangles and so determine their areas.
You can decompose the figure into two triangles. However, all you know about each triangle are the lengths of two of its sides. You need an additional piece of information - either the length of the third side (ie one of the diaongals of the quadrilateral) or an angle - in order to solve those triangles and so determine their areas.
FAQ: How to find the area of this irregular quadrilateral?
How do I find the area of an irregular quadrilateral?
To find the area of an irregular quadrilateral, you can use the formula A = ½ x (sum of opposite sides) x (distance between the opposite sides). This formula is also known as the "Brahmagupta's formula".
Can I use the same formula to find the area of any irregular quadrilateral?
Yes, the formula A = ½ x (sum of opposite sides) x (distance between the opposite sides) can be used to find the area of any irregular quadrilateral, regardless of its shape or size.
What if I don't know the distance between the opposite sides?
If you don't know the distance between the opposite sides, you can still find the area of the irregular quadrilateral by dividing it into smaller, simpler shapes (such as triangles or rectangles) and using their respective area formulas. Then, you can add the areas of these smaller shapes to find the total area of the irregular quadrilateral.
Is there a more accurate way to find the area of an irregular quadrilateral?
Yes, there are other methods to find the area of an irregular quadrilateral, such as the "shoelace formula" or using trigonometric functions. However, the formula A = ½ x (sum of opposite sides) x (distance between the opposite sides) is the most commonly used and accurate method.
Can I use a calculator to find the area of an irregular quadrilateral?
Yes, you can use a calculator to find the area of an irregular quadrilateral, as long as you have the necessary measurements (opposite sides and distance between them). However, it is always recommended to double-check your calculations to ensure accuracy.