how to find the area of a kite

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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.

1

Set up the formula for the area of a kite, given two diagonals. 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]
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] ^[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: $A={\frac {7\times 10}{2}}$ .
3

Multiply the lengths of the diagonals. The product becomes the new numerator in the area equation.^[6]
4

Divide the product of the diagonals by 2. This will give you the area of the kite, in square units.^[7]

1
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.
- 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.
4

Plug the angle measurement into the formula. Make sure you are using the angle between the two non-congruent sides.
5
Find the sine of the angle. To do this, you can use a calculator, or use a trigonometry chart.^[9]
- 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.

1

Set up the formula for the area of a kite, given two diagonals. 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.^[10]
2
Plug the area of the kite into the formula. This information should be given to you. Make sure you are substituting for $A$ .
- 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 $x$ .
- 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.
5

Divide each side of the equation by the length of the diagonal. This will give you the length of the missing diagonal.

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Question

How 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.

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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?

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?

That's not enough information to find the area.
Question

Are all diagonals equal?

No. 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.
Question

What is the area of a kite equal to?

The 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.
Question

What 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.
Question

How 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.
Question

How 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 one-half of the short diagonal (meaning one-quarter 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.
Question

How 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.
Question

Can 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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Article SummaryX

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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