# Area of a kite

Practice: Area of trapezoids. Area of kites. Finding area by rearranging parts. Area of composite shapes. Practice: Area of composite shapes. Practice: Area challenge. Next lesson. Current timeTotal duration CCSS Math: 6. Google Classroom Facebook Twitter. Video transcript What is the area of this figure? And this figure right over here is sometimes called a kite for obvious reasons.

If you tied some string here, you might want to fly it at the beach. And another way to think about what a kite is, it's a quadrilateral that is symmetric around a diagonal.

So this right over here is the diagonal of this quadrilateral. And it's symmetric around it. This top part and this bottom part are mirror images. And to think about how we might find the area of it given that we've been given essentially the width of this kite, and we've also been given the height of this kite, or if you view this as a sideways kite, you could view this is the height and that the eight centimeters as the width. Given that we've got those dimensions, how can we actually figure out its area?

So to do that, let me actually copy and paste half of the kite. So this is the bottom half of the kite. And then let's take the top half of the kite and split it up into sections.

So I have this little red section here. I have this red section here. And actually, I'm going to try to color the actual lines here so that we can keep track of those as well. So I'll make this line green and I'll make this line purple. So imagine taking this little triangle right over here-- and actually, let me do this one too in blue.

So this one over here is blue. You get the picture. Let me try to color it in at least reasonably. So I'll color it in. And then I could make this segment right over here, I'm going to make orange. So let's start focusing on this red triangle here. Imagine flipping it over and then moving it down here. So what would it look like? Well then the green side is going to now be over here.A kite is a four-sided shape with straight sides that has two pairs of sides.

Each pair of adjacent sides are equal in length. A square is also considered a kite. Each triangle has a height of. Express the area of the shape in terms of. The shape being described is a rhombus with side lengths 1.

## Advanced Geometry : How to find the area of a kite

Since they are equilateral triangles connected by one side, that side becomes the lesser diagonal, so. The greater diagonal is twice the height of the equaliteral triangles. The area of the kite is given below. The FOIL method will need to be used to simplify the binomial. What is the area? Find the area. We are given the length of these diagonals in the problem, so we can substitute them into the formula and solve for the area:.

Express the kite's area in simplified form. If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Hanley Rd, Suite St. Louis, MO Subject optional. Home Embed.JavaScript seems to be disabled in your browser. For the best experience on our site, be sure to turn on Javascript in your browser. There are few windy-day pastimes more fun than flying a kite. Whether you prefer diamond kites, fighter kites, or Hello Kitty kites they're all the rage nowflying them can make dull windy days infinitely more enjoyable.

### Area of a Kite

The kites we're referring to probably aren't the ones that David Tomlinson was singing about. Oh well. We already know that a kite is defined as a quadrilateral that has two adjacent pairs of congruent sides. If all four sides of a kite are congruent, then we just have a rhombus. That's all good and fine, but it doesn't seem like any of that will help us find the area.

But wait. If we can use the diagonals of a rhombus to find the area, can we do the same with kites? If the two diagonals of a kite are perpendicular to each other which they arethen we should be able to use the same type of formula. Let's take a look at this logically for a second. We can split the vertical diagonal into two sections as well, but we don't know exactly what ratio.

Since the area of the kite is the area of the four triangles combined, we can just add up the areas of the individual triangles. That means our final area formula for a kite ends up being relatively simple. She requests the diamond be a perfect cut, with diagonals of 3 mm and 5 mm. What is the area of the diamond's cross-section? All we need to do is apply the formula for the area of a kite.

We have the two diagonals, and that's all we need, right? One diagonal of a kite is three times as long as the other. The shorter diagonal splits the longer one so that two isosceles right triangles are formed. If the area of the kite is Welp, we know that we have to use the area formula, but we should relate the two diagonals to each other first. If d 1 is a certain length xthen d 2 is three times that length, 3 x. Plugging in these values to the area formula should give us the lengths of the diagonals.Familiarize students with another member of the quadrilateral family and escalate practice with these area of kites worksheets for grade 6, grade 7 and grade 8.

Based on the common core curriculum, these printable worksheets emphasize calculating the area of a kite using the formula with dimensions offered as integers, decimals and fractions, unit conversions and finding the missing parameters. Type 1 offers geometric representations while Type 2 includes problems in word format too. Get into gear with our free worksheets!

Area of a Kite Integers - Type 1. Find the Area of a Kite Integers - Type 2. Bolster practice with these area of a kite worksheets offering problems as figures and in word format with two levels. The diagonal lengths are given as integers, multiply them and divide by 2 to find the area.

Area of a kite Decimals. Find the product of the lengths of the two diagonals presented as decimals, half it, round the answer to 2 decimal places to solve for the area of the kites in these printable area of kite worksheets.

Area of a kite Fractions. Plug the diagonal lengths offered as fractions into the area formula to determine the area of the kites. Area of a Kite Unit Conversions. This set of unit conversion worksheets for 7th grade and 8th grade students specifies the lengths of the diagonals in varied units.

Convert the unit as per the requirement and apply the formula to find the area of the kite. Finding the diagonal of a kite. Featured here are problems that provide the area of the kite and the length of one diagonal. Assign the values in the formula to solve for the missing diagonal. The pdf worksheets cater to the learning needs of middle school students.

Members have exclusive facilities to download an individual worksheet, or an entire level. Login Become a Member. Select the Measurement Units U. Customary Units Metric Units. Two levels of difficulty with 5 worksheets each Download the set 10 Worksheets. Find the Area of a Kite Integers - Type 2 Bolster practice with these area of a kite worksheets offering problems as figures and in word format with two levels. Area of a kite Decimals Find the product of the lengths of the two diagonals presented as decimals, half it, round the answer to 2 decimal places to solve for the area of the kites in these printable area of kite worksheets.

Two different types with 5 worksheets each Download the set 10 Worksheets. Area of a kite Fractions Plug the diagonal lengths offered as fractions into the area formula to determine the area of the kites. Area of a Kite Unit Conversions This set of unit conversion worksheets for 7th grade and 8th grade students specifies the lengths of the diagonals in varied units.

Finding the diagonal of a kite Featured here are problems that provide the area of the kite and the length of one diagonal. Type: Integers, Decimals 5 worksheets each Download the set 10 Worksheets. What's New? Follow us. Not a Member?Although a rhombus is a type of parallelogramwhereas a kite is not, they are similar in that their sides have important properties. Recall that all four sides of a rhombus are congruent.

Kites, on the other hand, have exactly two pairs of consecutive sides that are congruent. This characteristic of kites does not allow for both pairs of opposite sides to be parallel. Let's look at the image below to examine the properties that make these figures distinguishable. Despite how different they are, when it comes to areawe will see that rhombuses and parallelograms are quite similar.

The areas of rhombuses and kites are equal to one half the product of their diagonals. Mathematically, we express this as.

Kites, Basic Introduction, Geometry

Recall that every quadrilateral has exactly two diagonals. This is because diagonals are line segments which connect vertices to each other.

Since there already exist line segments which connect one vertex to two other vertices in a quadrilateral, the only other line segment to draw is to the vertex diagonal from the chosen vertex.

Let's work on the following exercises, to help us apply the area formula for rhombuses and kites. The only two parts of the rhombus we need to figure out are the diagonals because that is all that is required when we find the areas of rhombuses. We are given the length of one diagonal of rhombus PQRSwhich will be our d 1.

## How to Calculate the Area of a Kite

The length of diagonal PR is 12 centimeters. Before we can find the area of rhombus PQRSwe need to find the length of d 2. We see that the length of SQis just the sum of two smaller segments. However, we do not know what the length of TQ is, so we must rely on our knowledge of rhombuses to help us out at this point.

We know that the diagonals of a rhombus bisect each other. This means that the point T is the midpoint of segment SQ. Thus, we know that the length of segment TQ is equal to the length of segment ST ; they are both 4 centimeters long.

Now, we can find the length of SQwhich is our d 2 :. So, we know that d 2 has a length of 8 centimeters. Now, we have all the requirements we need in order to solve for the area of rhombus PQRS.

Let's plug our values of d 1 and d 2 in:. We see that rhombus PQRS has an area of 48 square centimeters. Find the value of y given that the area of kite YDOC is square feet. In this exercise, we will not be solving for area, since it has already been given to us.If you are looking for the formula for kite area or perimeter, you're in the right place: the kite area calculator is here to help you.

Whether you know the length of the diagonals or two unequal side lengths and the angle between, you can quickly calculate the area of a kite. For kite perimeter all you need to do is entering two kite sides. But if you are still wondering how to find the area of a kite, keep scrolling! If it's not a kite area you are looking for, check our kiteboarding calculatorwhich can help with the choice of the proper kite size for you. Kite is a quadrilateral with two pairs of equal-length sides, adjacent to each other.

Kite is a symmetric shape and its diagonals are perpendicular. There are two basic kite area formulas, which can be used depending on which information you have:. If you know two non-congruent side lengths and the size of the angle between those two sides, use the formula:. Did you notice that it's a doubled formula for the triangle areaknowing side-angle-side? Yes, that's right! Kite is a symmetric quadrilateral and can be treated as two congruent triangles that are mirror images of each other.

To calculate the kite perimeter, you need to know two unequal sides. Then, the formula is obvious:. You can't calculate the perimeter knowing only the diagonals - we know that one is a perpendicular bisector of the other diagonal, but we don't know where is the intersection. Let's imagine we want to make a simple, traditional kite. And if we're going to make an edging from a ribbon, what length is required? The answer is almost always no. It's working the other way round - every rhombus is a kite. Only if all four sides of a kite have the same length, it must be a rhombus - or even a square, if additionally all the angles are right.During these challenging times, we guarantee we will work tirelessly to support you.

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Updated: September 25, References. A kite is a type of a quadrilateral that has two pairs of equal, adjacent sides. 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. 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! Did this summary help you? Yes No. Log in Facebook Loading Google Loading Civic Loading No account yet?

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Together, they cited information from 7 references. Learn more Using the Area to Find a Missing Diagonal. Things You'll Need. Related Articles.