A kite is a type of a quadrilateral that has two pairs of equal, adjacent sides. [1] X Research source Kites can take the traditional look of a flying kite, but a kite can also be a rhombus or a square. [2] X Research source No matter what a kite looks like, the methods for finding the area will be the same. If you know the length of the diagonals, you can find the area through simple algebra. You can also use trigonometry to find the area, if you know the side and angle measurements of the figure.
Steps
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Set up the formula for the area of a kite, given two diagonals. The formula is , where equals the area of the kite, and and equal the lengths of the diagonals of the kite. [3] X Research source
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Plug the lengths of the diagonals into the formula. A diagonal is a straight line that runs from one vertex to the vertex on the opposite side. [4] X Expert Source David Jia
Academic Tutor Expert Interview. 23 February 2021 [5] X Research source You should either be given the length of the diagonals, or be able to measure them. If you don’t know the length of the diagonals, you cannot use this method.- For example, if a kite has two diagonals measuring 7 inches and 10 inches, your formula will look like this: .
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Multiply the lengths of the diagonals. The product becomes the new numerator in the area equation. [6] X Expert Source David Jia
Academic Tutor Expert Interview. 23 February 2021- For example:
- For example:
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Divide the product of the diagonals by 2. This will give you the area of the kite, in square units. [7] X Expert Source David Jia
Academic Tutor Expert Interview. 23 February 2021- For example:
So, the area of a kite with diagonals measuring 10 inches and 7 inches is 35 square inches.
- For example:
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Set up the formula for the area of a kite. This formula works if you are given two non-congruent side lengths and the size of the angle between those two sides. The formula is , where equals the area of the kite, and equal the non-congruent side lengths of the kite, and equals the size of the angle between sides and . [8] X Research source
- Make sure you are using two non-congruent side lengths. A kite has two pairs of congruent sides. You need to use one side from each pair. Make sure the angle measurement you use is the angle between these two sides. If you do not have all of this information, you cannot use this method.
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Plug the length of the sides into the formula. This information should be given, or you should be able to measure them. Remember that you are using non-congruent sides, so each side should have a different length. [9] X Research source
- For example, if your kite has a side length of 20 inches and a side length of 15 inches, your formula will look like this: .
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Multiply the side lengths. Plug this product into the formula.
- For example:
- For example:
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Plug the angle measurement into the formula. Make sure you are using the angle between the two non-congruent sides.
- For example, if the angle measurement is , your formula will look like this: .
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Find the sine of the angle. To do this, you can use a calculator, or use a trigonometry chart. [10] X Research source
- For example, the sine of a 150 degree angle is .5, so your formula will look like this: .
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Multiply the product of the sides by the sine of the angle. This result will be the area of the kite, in square units. [11] X Research source
- For example:
So, the area of a kite, with two sides measuring 20 inches and 15 inches, and the angle between them measuring 150 degrees, is 150 square inches.
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Set up the formula for the area of a kite, given two diagonals. The formula is , where equals the area of the kite, and and equal the lengths of the diagonals of the kite. [12] X Research source
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Plug the area of the kite into the formula. This information should be given to you. Make sure you are substituting for .
- For example, if your kite has an area of 35 square inches, your formula will look like this: .
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Plug the length of the known diagonal into the formula. Substitute for .
- For example, if you know one of the diagonals is 7 inches long, your formula will look like this: .
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Multiply each side of the equation by 2. This will remove the fraction in the formula. [13] X Research source
- For example:
- For example:
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Divide each side of the equation by the length of the diagonal. This will give you the length of the missing diagonal. [14] X Research source
- For example:
So, the length of the missing diagonal of a kite, given an area of 35 square inches and one diagonal of 7 inches, is 10 inches.
- For example:
Expert Q&A
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QuestionHow do I find the diagonals of a kite?David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.Measure from one corner to the corner directly across from it to find the length of a diagonal.
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QuestionHow do I find the measure of the diagonals of a kite if I only have the area?Community AnswerThis isn't possible without more information. If you knew the size of one of the angles, or the length of one side, you might be able to find the length of the diagonals using the Pythagorean Theorem. If you know the relationship between the diagonal lengths (for example, one diagonal is twice as long as the other) and the area, you can use algebra to find the length of the diagonals.
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QuestionHow to find the area of a kite given the length of the sides?DonaganTop AnswererThat's not enough information to find the area.
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References
- ↑ http://www.mathopenref.com/kite.html
- ↑ https://www.mathsisfun.com/geometry/kite.html/
- ↑ https://www.mathsisfun.com/geometry/kite.html
- ↑ David Jia. Academic Tutor. Expert Interview. 23 February 2021
- ↑ http://www.mathopenref.com/diagonal.html
- ↑ David Jia. Academic Tutor. Expert Interview. 23 February 2021
- ↑ David Jia. Academic Tutor. Expert Interview. 23 February 2021
- ↑ http://www.mathopenref.com/kitearea.html
- ↑ https://www.omnicalculator.com/math/kite-area
- ↑ https://mathmonks.com/kite/area-of-a-kite
- ↑ https://mathmonks.com/kite/area-of-a-kite
- ↑ https://www.mathsisfun.com/geometry/kite.html
- ↑ https://www.varsitytutors.com/advanced_geometry-help/how-to-find-the-length-of-the-diagonal-of-a-kite
- ↑ https://www.varsitytutors.com/advanced_geometry-help/how-to-find-the-length-of-the-diagonal-of-a-kite
About This Article
You can easily find the area of a kite if you know the lengths of the diagonals, or the two lines that connect each of the adjacent vertices (corners) of the kite. If you know the lengths of these diagonals, you can plug them into the formula A (area) = xy/2, where x and y are the two diagonals. For example, if you have a kite with a diagonal of 7 inches and another diagonal of 10 inches, the area of the kite would equal (7 x 10)/2, or 35 square inches. If you don’t know the lengths of the diagonals, you can find the area of the kite using the lengths of two non-congruent sides (that is, two sides that are not of the same length) and the size of the angle between them. To do this, use the formula A = a x b x sinC, where a and b are the lengths of the sides and C is the angle between them. For instance, say you have a kite with two sides that are 20 and 15 inches long, with an angle of 150° between them. The area of the kite equals 20 x 15 x sin150°, which equals 300 x sin150°, or 150 square inches. To learn how to use the angle of the kite to find the length of a missing diagonal, read on!
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