This article was coauthored 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.
There are 7 references cited in this article, which can be found at the bottom of the page.
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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
Method 1
Method 1 of 3:Using the Diagonals to Find the Area

1Set 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 }

2Plug 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 JiaAcademic 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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3Multiply the lengths of the diagonals. The product becomes the new numerator in the area equation.^{[6] X Expert Source David JiaAcademic Tutor Expert Interview. 23 February 2021 }
 For example:
 For example:

4Divide the product of the diagonals by 2. This will give you the area of the kite, in square units.^{[7] X Expert Source David JiaAcademic 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.
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Method 2
Method 2 of 3:Using an Angle and Two Sides to Find the Area

1Set up the formula for the area of a kite. This formula works if you are given two noncongruent 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 noncongruent 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 noncongruent 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.

2Plug 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 noncongruent sides, so each side should have a different length.
 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: .

3Multiply the side lengths. Plug this product into the formula.
 For example:
 For example:

4Plug the angle measurement into the formula. Make sure you are using the angle between the two noncongruent sides.
 For example, if the angle measurement is , your formula will look like this: .

5Find the sine of the angle. To do this, you can use a calculator, or use a trigonometry chart.^{[9] X Research source }
 For example, the sine of a 150 degree angle is .5, so your formula will look like this: .

6Multiply the product of the sides by the sine of the angle. This result will be the area of the kite, in square units.
 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

1Set 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.^{[10] X Research source }

2Plug 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: .

3Plug 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: .

4Multiply each side of the equation by 2. This will remove the fraction in the formula.
 For example:
 For example:

5Divide each side of the equation by the length of the diagonal. This will give you the length of the missing diagonal.
 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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Community Q&A

QuestionHow do I find the diagonals of a kite?David JiaDavid 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.
Academic TutorMeasure from one corner to the corner directly across from it to find the length of a diagonal. 
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.

QuestionHow to find the area of a kite given the length of the sides?That's not enough information to find the area.

QuestionAre all diagonals equal?Community AnswerNo. Although the diagonals could be equal, a kite shape (roughly a diamond shape) has two typically unequal diagonals. If they were equal, the shape would be a square.

QuestionWhat is the area of a kite equal to?Community AnswerThe area of a kite measures the space inside the four sides. The most common way to find the area is by using the formula A = xy/2, where x and y are the lengths of the diagonals.

QuestionWhat is the ratio of diagonals in a kite?There is no standard ratio. A kite can be made to any specifications, so the diagonals can be any length. A typical ratio, however, would be roughly 3:2.

QuestionHow do I calculate the diagonal length of a kite if I know the length of the sides?You would need additional information such as the area of the kite or two of the angles.

QuestionHow do I find the area of a kite by splitting it into triangles?A kite's longer diagonal splits the kite into two triangles of equal area. You can find the kite's area by finding the area of either triangle and doubling it. The area of either triangle is half the product of the long diagonal and onehalf of the short diagonal (meaning onequarter of the product of the two diagonals). So the area of the full kite is twice that product, which means half the product of the two diagonals.

QuestionHow do I find the area of a kite when I don't have the measurement, only the area of an isosceles of it?A kite shape consists of two isosceles triangles. If you know the areas of both of them, add them together to get the kite's area.

QuestionCan the volume of a kite be calculated?No, not a kite as described in this article. There are box kites and certain other shapes that could be said to define a volume. For a box kite you would multiply length by width by height.
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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
 ↑ http://www.mathmistakes.info/facts/TrigFacts/learn/vals/sum.html
About This Article
To find the area of a kite using the 2 diagonals, measure the length of the diagonals. Label these 2 lines x and y. Multiply the lengths of x and y, then divide the result by 2 to get the area of the kite. If you have the area and the lengths of 2 sides, multiply the length of side a times the length of side b, then multiply that by the sin of the angle, or C. To learn how to use the angle of the kite to find the length of a missing diagonal, read on!
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