How to Find the Area of a Kite

Co-authored by David Jia

Last Updated: November 28, 2022 Fact Checked

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

Method 1

Method 1 of 3:

Using the Diagonals to Find the Area

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The formula is $A={\frac {xy}{2}}$ , where $A$ equals the area of the kite, and $x$ and $y$ equal the lengths of the diagonals of the kite.^{[3]
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Research source}
2
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]
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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: $A={\frac {7\times 10}{2}}$ .
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3
Multiply the lengths of the diagonals. The product becomes the new numerator in the area equation.^{[6]
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David Jia
Academic Tutor

Expert Interview. 23 February 2021}
- For example:
  $A={\frac {7\times 10}{2}}$
  $A={\frac {70}{2}}$
4
Divide the product of the diagonals by 2. This will give you the area of the kite, in square units.^{[7]
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Expert Source

David Jia
Academic Tutor

Expert Interview. 23 February 2021}
- For example:
  $A={\frac {70}{2}}$
  $A=35$
  So, the area of a kite with diagonals measuring 10 inches and 7 inches is 35 square inches.

Method 2

Method 2 of 3:

Using an Angle and Two Sides to Find the Area

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1
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 $A=ab\sin C$ $A=ab\sin C$ , where $A$ $A$ equals the area of the kite, $a$ $a$ and $b$ $b$ equal the non-congruent side lengths of the kite, and $C$ $C$ equals the size of the angle between sides $a$ $a$ and $b$ $b$ .^{[8]
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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.
2
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]
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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: $A=20\times 15\sin C$ .
3
Multiply the side lengths. Plug this product into the formula.
- For example:
  $A=20\times 15\sin C$
  $A=300\sin C$
4
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 $150^{\circ }$ , your formula will look like this: $A=300\sin(150)$ .
5
Find the sine of the angle. To do this, you can use a calculator, or use a trigonometry chart.^{[10]
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Research source}
- For example, the sine of a 150 degree angle is .5, so your formula will look like this: $A=300(.5)$ .
6
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]
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Research source}
- For example:
  $A=300(.5)$
  $A=150$
  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.

Method 3

Method 3 of 3:

Using the Area to Find a Missing Diagonal

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The formula is $A={\frac {xy}{2}}$ , where $A$ equals the area of the kite, and $x$ and $y$ equal the lengths of the diagonals of the kite.^{[12]
X
Research source}
2
Plug the area of the kite into the formula. This information should be given to you. Make sure you are substituting for $A$ $A$ .
- For example, if your kite has an area of 35 square inches, your formula will look like this: $35={\frac {xy}{2}}$ .
3
Plug the length of the known diagonal into the formula. Substitute for $x$ $x$ .
- For example, if you know one of the diagonals is 7 inches long, your formula will look like this: $35={\frac {7y}{2}}$ .
4
Multiply each side of the equation by 2. This will remove the fraction in the formula.^{[13]
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Research source}
- For example:
  $35={\frac {7y}{2}}$
  $35\times 2={\frac {7y}{2}}\times 2$
  $70=7y$
5
Divide each side of the equation by the length of the diagonal. This will give you the length of the missing diagonal.^{[14]
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Research source}
- For example:
  $70=7y$
  ${\frac {70}{7}}={\frac {7y}{7}}$
  $10=y$
  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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Question

How do I find the diagonals of a kite?

David Jia
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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.

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Expert Answer

Measure from one corner to the corner directly across from it to find the length of a diagonal.

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Question

How do I find the measure of the diagonals of a kite if I only have the area?

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.

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How to find the area of a kite given the length of the sides?

Donagan

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That's not enough information to find the area.

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