Area of a Kite Calculator

Welcome to our Area of a Kite Calculator page.

We explain how to find the area of a kite and provide a quick calculator to work it out for you, step-by-step.

You can also use our calculator to find the area of a dart which is an concave kite.

There are also some worked examples and some worksheets for you to practice this skill.

Area of a Kite Calculator

This calculator finds the area of a kite when the diagonal lengths are known.

The major diagonal forms a line of symmetry for the kite and bisects the minor diagonal.

Area of a Kite Calculator

area of a kite labelled image


Answer


Answer

 
 


How the Calculator Works

  1. Choose the major diagonal length and minor diagonal length of the kite: you can choose a whole number, decimal or fraction.
    • You can type a fraction by typing the numerator then '/' then the denominator.
    • You can type a mixed number by typing the whole-number part, then a space then the fraction part.
    • Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).
  2. Choose your units of measurement (default is none)
  3. Choose your desired accuracy (default is 2 decimal places)
  4. Click the Find Area button
  5. You will be shown the area as a decimal (and also a fraction if you typed the length as a fraction).

Area of a Kite Formula

area of a kite formula image

The formula for the area of a kite or a dart (which is a concave kite) is: \[ A = {1 \over 2} ab \; \]

where A is the area of the kite, a is the major diagonal length and b is the minor diagonal length of the kite

Area of a Kite Explanation

First let's look at the kite below.

area of a kite labelled image

Now we are going to cut the kite in half along the major diagonal.

area of a kite formula 1 image

Next we are going to put the half-kite inside a blue rectangle..

area of a kite formula 2 image

You can see the half-kite forms a triangle which takes up exactly half of the area of the blue rectangle it is inside.

So the full size kite, which has twice the area of the half-size kite, will take up the whole area of the blue rectangle which the half-size kite is inside.

So the area of the blue rectangle and the area of the whole kite are equal.

The blue rectangle has the length of the major diagonal (a) and the width of half of the minor diagonal (½ b).

To find the area of the blue rectangle, we multiply the adjacent sides together which gives us:

\[ Area = a \cdot {1 \over 2} b = {1 \over 2} ab \]

Area of a Kite Examples


Area of a Kite Example 1

Find the area of the kite below.

area of a kite example 1

The major diagonal length is 8 cm and the minor diagonal length is 5 cm.

The area of a kite

\[ A = {1 \over 2} ab \; \] where a is the major diagonal length and b is the minor diagonal length.

So if we substitute the values of the length and width into this equation, we get: \[ A = {1 \over 2} \cdot 5 \cdot 8 = {1 \over 2} \cdot 40 = 20 \]

The area of the kite is 20 cm2.

Area of a Kite Example 2

Find the area of the kite below.

area of a kite example 2

The major diagonal length is 1.3 m and the minor diagonal length is 0.9 m.

The area of a kite

\[ A = {1 \over 2} ab \; \] where a is the major diagonal length and b is the minor diagonal length.

So if we substitute the values of the length and width into this equation, we get: \[ A = {1 \over 2} \cdot 1.3 \cdot 0.9 = {1 \over 2} \cdot 1.17 = 0.585 \]

The area of the kite is 0.585 m2.

Area of a Kite Example 3

Find the area of the dart below.

area of a kite example 3

The major diagonal length is 1.3 m and the minor diagonal length is 0.9 m.

The area of a kite

\[ A = {1 \over 2} ab \; \] where a is the major diagonal length and b is the minor diagonal length.

So if we substitute the values of the length and width into this equation, we get: \[ A = {1 \over 2} \cdot 11 \cdot 15 = {1 \over 2} \cdot 165 = 82.5 \]

The area of the kite is 82.5 cm2.

Area of a Kite Example 4

Find the area of the kite below, giving your answer to 2 decimal places.

area of a kite example 4

The major diagonal length is 1.3 m and the minor diagonal length is 0.9 m.

The area of a kite

\[ A = {1 \over 2} ab \; \] where a is the major diagonal length and b is the minor diagonal length.

So if we substitute the values of the length and width into this equation, we get: \[ A = {1 \over 2} \cdot 5 {1 \over 2} \cdot 3 {1 \over 4} = {1 \over 2} \cdot 17 {7 \over 8} = 8.9375 \]

The area of the kite is 8.94 in2 to 2 decimal places.

Area of a Kite Worksheets

We have 2 worksheets to help you practice finding the area of different kites and darts.

The first sheet is slightly easier, and contains whole numbers and fractional values only.

The second sheet contains whole numbers and both fractional and decimal values.

More Area Support and Resources

We have a range of other area worksheets and support pages for a range of different 2d shapes.

More Area & Volume Calculators

We have a range of area and volume calculators to help you find the area and volumes of a range of different 2d and 3d shapes.

Each calculator page comes with worked examples, formulas and practice worksheets.

Looking for more math calculators?

We have a wide range of free math calculators to help you.

Most of our calculators show you their working out so that you can see exactly what they have done to get the answer.

Our calculator hub page contains links to all of our calculators!

 

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