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Area of a Kite: Formula & Examples

Area of a Kite: Formula & Examples
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  • 0:03 What Is a Kite?
  • 0:39 Area of a Kite
  • 2:02 More Practice
  • 3:04 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

In this lesson, we'll learn the mathematical definition of a kite and see what this shape looks like. We'll then take things a step further and learn how to use a formula to find the area of a kite.

What Is a Kite?

Suppose you look out the window and realize it's a perfect day to go to the park and fly a kite. You call up your friends and get together only to realize you don't have a kite. You all decide to build one from two pieces of light-weight wood and some fabric. In mathematics, we describe a kite as a four-sided, two-dimensional object with two pairs of equal sides that each share an angle.

The shorter of the two pieces of wood has a length of 20 inches, and the longer piece has a length of 28 inches. You're planning on connecting your fabric to the pieces of wood in the shape of a kite. The only problem is that you don't know how much fabric you need to make your kite.

Area of a Kite

Diagonals of the kite
areakite4

Mathematically speaking, the area of a kite is the size of its surface. Therefore, in the case of building your kite, the area of the kite is the size of the fabric needed to build your kite. This is specifically what we need to know in order to build it. Well, there's great news! We have all the information we need in order to find the area of your kite!

Once again, mathematically speaking, we would call the pieces of wood in our kite diagonals. Diagonals are the two lines that run perpendicular to one another that connect the angles across form each other in a kite. To find the area of a kite, we have an easy-to-use formula that only requires us to know the lengths of the diagonals of the kite.

areakite2

See! We do have all the information we need to find the area of our kite! We have the length of the diagonals, or our pieces of wood. Those are 20 inches and 28 inches. Thus, we simply plug these values into our formula and simplify.

Since the area equals diagonal 1 times diagonal 2, divided by 2, when we plug in the values of the diagonals, we get:

(20 * 28) / 2 = 280 in2

See how easy that is? We see that we need 280 square inches of fabric to build our kite. Let's look at a few more examples to really drive the use of this formula home!

More Practice

Example 1

areakite3

Suppose we want to find the area of a kite with diagonals of 12 inches and 18 inches. We simply plug these values into our formula and evaluate:

Area = (d1 * d2) / 2 = (12 * 18) / 2 = 108

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