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A kite is a type of a quadrilateral that has two pairs of equal, adjacent sides.[1] Kites can take the traditional look of a flying kite, but a kite can also be a rhombus or a square.[2] 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.

Method 1
Method 1 of 3:

Using the Diagonals to Find the Area

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  1. The formula is , where equals the area of the kite, and and equal the lengths of the diagonals of the kite.[3]
  2. A diagonal is a straight line that runs from one vertex to the vertex on the opposite side.[4] [5] 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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  3. The product becomes the new numerator in the area equation.[6]
    • For example:

  4. This will give you the area of the kite, in square units.[7]
    • For example:


      So, the area of a kite with diagonals measuring 10 inches and 7 inches is 35 square inches.
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Method 2
Method 2 of 3:

Using an Angle and Two Sides to Find the Area

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  1. 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]
    • 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.
  2. 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]
    • 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: .
  3. Plug this product into the formula.
    • For example:

  4. 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: .
  5. To do this, you can use a calculator, or use a trigonometry chart.[10]
    • For example, the sine of a 150 degree angle is .5, so your formula will look like this: .
  6. This result will be the area of the kite, in square units.[11]
    • 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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Method 3
Method 3 of 3:

Using the Area to Find a Missing Diagonal

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  1. The formula is , where equals the area of the kite, and and equal the lengths of the diagonals of the kite.[12]
  2. 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: .
  3. Substitute for .
    • For example, if you know one of the diagonals is 7 inches long, your formula will look like this: .
  4. This will remove the fraction in the formula.[13]
    • For example:


  5. This will give you the length of the missing diagonal.[14]
    • 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.
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Expert Q&A

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  • Question
    How do I find the diagonals of a kite?
    David Jia
    David Jia
    Academic Tutor
    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.
    David Jia
    Academic Tutor
    Expert Answer
    Measure from one corner to the corner directly across from it to find the length of a diagonal.
  • Question
    How do I find the measure of the diagonals of a kite if I only have the area?
    Community Answer
    Community Answer
    This 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.
  • Question
    How to find the area of a kite given the length of the sides?
    Donagan
    Donagan
    Top Answerer
    That's not enough information to find the area.
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References

  1. http://www.mathopenref.com/kite.html
  2. https://www.mathsisfun.com/geometry/kite.html/
  3. https://www.mathsisfun.com/geometry/kite.html
  4. David Jia. Academic Tutor. Expert Interview. 23 February 2021
  5. http://www.mathopenref.com/diagonal.html
  6. David Jia. Academic Tutor. Expert Interview. 23 February 2021
  7. David Jia. Academic Tutor. Expert Interview. 23 February 2021
  8. http://www.mathopenref.com/kitearea.html
  9. https://www.omnicalculator.com/math/kite-area

About This Article

David Jia
Co-authored by:
Academic Tutor
This article was co-authored by David Jia. 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. This article has been viewed 271,646 times.
38 votes - 69%
Co-authors: 15
Updated: November 28, 2022
Views: 271,646
Article SummaryX

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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