Geometry

##### Related Lessons

- 3 4 5 Triangle
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- Arc Length Calculator
- Area of a Circle Calculator
- Area of a Hexagon
- Area of a Kite
- Area of a Parallelogram
- Area of a Pentagon
- Area of a Rectangle
- Area of a Rhombus
- Area of a Sector
- Area of a Semicircle
- Area of a Square
- Area of a Trapezoid
- Area of a Triangle
- Center of Mass Calculator
- Circumference Calculator
- Distance Formula
- Distance Formula Calculator
- Geometry Calculators
- How to Find the Height of a Triangle
- Isosceles Triangle Theorem
- Law of Cosines Calculator
- Perimeter of a Circle
- Perimeter of a Pentagon
- Perimeter of a Rectangle
- Perimeter of a Rhombus
- Perimeter of a Semicircle
- Perimeter of a Square
- Perimeter of a Trapezoid
- Perimeter of a Triangle
- Properties of a Parallelogram
- Pythagorean Theorem Calculator
- Side Angle Side Theorem
- Side Splitter Theorem
- Similar Triangles
- Special Right Triangles
- Surface Area of a Cone
- Surface Area of a Cube
- Surface Area of a Cylinder
- Surface Area of a Hemisphere
- Surface Area of a Pyramid
- Surface Area of a Sphere
- Surface Area of a Triangular Prism
- Triangle Inequality Theorem
- Types of Triangles
- Vertical Angles
- Volume of a Cone
- Volume of a Cube
- Volume of a Hexagonal Prism
- Volume of a Pyramid
- Volume of a Sphere
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Tutors/teachers:

Nikkolas

Tutor and Aerospace Engineer

# Area of a Kite

## Kite Area Formula

A kite is a quadrilateral with two pairs of equal-length sides. The equal length sides are always opposite each other. There are two simple formulas for finding the area of a kite. They are given as:**1.) A = d _{1}d_{2}/2**

**2.) A = absin(c)**

Where

*A*is the area,

*d*is the long diagonal,

_{1}*d*is the short diagonal,

_{2}*a*is the short side,

*b*is the long side, and

*c*is the angle between short and long sides.

The diagonals method can be considered the simpler of the two because it only involves two basic length values. The trigonometry method requires us to know the angle between unequal sides. See the image below for how these dimensions within a kite are notated.

### Formula 1: Using the Diagonals to Find Area

If we know the diagonals of a kite, we can use the diagonals formula to find area. The formula is given as:**A = d _{1}d_{2}/2**

Where

*d*is the long diagonal and

_{1}*d*is the short diagonal.

_{2}Here’s an example of using this formula for a kite with a long diagonal length of 4 and short diagonal length of 2.

A = d_{1}d_{2}/2

A = (4)(2)/2 = 8/2 = 4

### Formula 2: Using Trigonometry to Find Area

If we know the side lengths and angle between unequal sides, we can use trigonometry to find area of a kite. The formula for this is given as:**A = absin(c)**

Where *a* is the length of the short side, *b* is the length of the long side, and *c* is the internal angle between those two sides.

Here’s an example of using this formula for a kite with a side *a* length of 4, a side *b* length of 7, and an internal angle *c* value of 100 degrees.

A = absin(c)

A = (4)(7)sin(100°) = (28)(0.9848) = 27.574

Result :

Worksheet 1

Download.pdf

Cheat sheet

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