The Area Of A Kite

Kite Expanse Calculator

Created by Hanna Pamuła , PhD candidate

Reviewed past

Bogna Szyk and Steven Wooding

Final updated:

Sep 12, 2022

Table of contents:

Kite surface area formula
Kite perimeter
How to find the expanse of the kite? How most kite perimeter?
Convex and concave kites
Is kite a rhombus?

If you lot are looking for the formula for kite area or perimeter, you're in the right place: the kite area calculator is here to help y'all. Whether you know the length of the diagonals or ii diff side lengths and the bending between, you can quickly calculate the area of a kite. For the kite perimeter, all you need to practice is enter two kite sides. But if you are still wondering how to notice the area of a kite, continue scrolling!

If it's non a kite area you are looking for, check our kiteboarding calculator, which can assist you lot choose the proper kite size.

Kite expanse formula

A kite is a quadrilateral with two pairs of equal-length sides adjacent to each other. A kite is a symmetric shape, and its diagonals are perpendicular. There are two bones kite area formulas, which y'all can use depending on which information you have:

If y'all know two diagonals, you can calculate the surface area of a kite every bit:

area = (east × f) / two , where due east and f are kite diagonals.

kite with sides a and b and angle α between them

If yous know two non-congruent side lengths and the size of the angle between those 2 sides, employ the formula:

area = a × b × sin(α), where α is the angle between sides a and b.

Did you detect that it's a doubled formula for the triangle expanse, knowing side-angle-side? Aye, that'southward right! A kite is a symmetric quadrilateral and can be treated as two coinciding triangles that are mirror images of each other.

Kite perimeter

To summate the kite perimeter, you demand to know ii unequal sides. Then, the formula is obvious:

perimeter = a + a + b + b = two × (a + b)

You can't calculate the perimeter knowing simply the diagonals – we know that one is a perpendicular bisector of the other diagonal, but we don't know where is the intersection.

How to find the area of the kite? How well-nigh kite perimeter?

Permit's imagine we want to brand a simple, traditional kite. How much newspaper/foil do we need? And if nosotros're going to make an edging from a ribbon, what length is required?

Think for a while and choose the formula which meets your needs. Assume we constitute two sticks in the wood; let'due south use them for our kite!
Enter the diagonals of the kite. The ones we have are 12 and 22 inches long.
Area of a kite appears below. It's 132 in².

image of a kite from the example, with diagonals of 12 and 22

Calculation of the kite perimeter is a bit tricky in that case. Let'due south take a wait:

Assume you've chosen the final kite shape – you've decided where the diagonals intersect each other. For example, the shorter ane will be split in the eye (six in : 6 in) and the longer i in the eight:xiv ratio, as shown in the motion-picture show.
Side by side, the easiest way is to employ our right triangle figurer (this method works only for convex kites). Type 6 and 8 as a and b – the hypotenuse is 1 of our kite sides, hither equal to 10 in. Refresh the calculator and enter 6 and fourteen – the result is 15.23 in, and that's our other side.
Here yous go! Equally we know both sides, we can summate the perimeter. Blazon the a and b sides. The result for our case is 50.46 in. So buy a little bit more ribbon than that, for example, 55 inches, to make the edging.

Convex and concave kites

The kite tin can be convex – it's the typical shape nosotros associate with the kite – or concave; such kites are sometimes called a dart or arrowheads. The area is calculated in the aforementioned fashion, merely you need to remember that i diagonal is at present "outside" the kite. The kite area calculator will work properly too for the concave kites.

Is kite a rhomb?

The reply is almost always no. It'southward working the other mode round – every rhombus is a kite. Simply if all four sides of a kite have the same length, it must be a rhombus – or even a square, if all the angles are right.

Hanna Pamuła , PhD candidate

kite with diagonals e and f