The area of the kite can be calculated by multiplying **the lengths of the diagonals and dividing this product by** **$2$****.**

The area of the kite can be calculated by multiplying **the lengths of the diagonals and dividing this product by** **$2$****.**

To facilitate the understanding of the concept of calculus, you can use the following drawing and the accompanying formula:

**$A=\frac{ KM\times NL}{2}$**

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

There are many geometric shapes that can be found during the solving of engineering problems at all different stages of study, such as in high school, in matriculation exams, and even in psychometry. One of the less trivial shapes is the deltoid and, as part of the questions surrounding it, students are often asked to calculate the area of the deltoid.

**A deltoid is a polygon with four sides (that is, a quadrilateral) with two distinct sets of adjacent sides of equal length to each other.**

Test your knowledge

Question 1

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

AD = 12

CB = 16

Calculate the area of the deltoid.

Question 2

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

Question 3

Given the kite ABCD

diagonal DB=10

CB=4

Is it possible to calculate the area of the kite? If so, what is it?

There is a clear distinction between **convex deltoid** and **concave deltoid**.

**Convex deltoid** is a deltoid where the diagonals are inside and cross each other. The longer diagonal acts as a **main diagonal**, while the shorter diagonal acts as a **secondary diagonal**.

As you can observe in the following drawing, the main diagonal divides the deltoid into two overlapping triangles, that is, identical, and the secondary diagonal divides the deltoid into two isosceles triangles whose bases are adjacent and, indeed, identical.

Do you know what the answer is?

Question 1

Given the deltoid ABCD

Find the area

Question 2

Given the deltoid ABCD

Find the area

Question 3

Given the deltoid ABCD

Find the area

**Concave kite** is a kite where one of the diagonals (**main diagonal**) passes inside the kite and the other diagonal (**secondary diagonal**) passes outside the kite.

The concave deltoid can be described as a shape consisting of two isosceles triangles that share a common base, where one triangle contains the other triangle. The following drawing better describes the concave deltoid:

- When all sides of the kite have the same length, a
**rhombus**is obtained, which is actually a special case of a kite. - Another special case of a kite is a
**square**, when it is a case where all sides and all angles are of the same size.

- The angles on the sides, or more precisely, the angles between the different adjacent sides of the kite, are of equal size.
- The diagonals of the kite are perpendicular to each other
- The main diagonal in the convex kite (or its extension in the concave kite) crosses the secondary diagonal (in both cases), and therefore actually functions as a perpendicular bisector
- The main diagonal equally divides (crosses) the main angles of the kite
- Every convex kite has the possibility of enclosing a circle
- In every kite, there are two sets of adjacent sides of equal size
- As mentioned, a concave kite is characterized by a secondary diagonal located outside of it

Check your understanding

Question 1

Given the deltoid ABCD

Find the area

Question 2

Given the deltoid ABCD

Find the area

Question 3

Given the deltoid ABCD

Find the area

The area of the kite must be calculated according to the attached drawing and the existing data:

- $BK= 3 cm$
- $AC= 7 cm$

**Solution**:

According to the kite area formula, we are missing the length of the diagonal $BD$.

We know that the diagonal $BK$ is equal to $3$ cm, and according to one of the properties of the kite, the diagonal $AC$ divides the diagonal $BD$ into two equal parts.

That is, from this we can conclude that $BD=6$.

$A=\frac{(AC\times BD)}{2}=\frac{(7\times6)}{2}=21$

At this point, we can place the data in the area formula and obtain:

**Answer**:

The area of the kite $ABCD$ is $21$ cm².

Given the kite $KLMN$ whose area is $144$ cm², the meeting point of the diagonals $LN$ and $KM$.

The area of the section KP must be calculated according to the attached drawing and the existing data:

- $LN=18$ cm
- $A=144$ cm²

**Solution:**

This exercise is a reverse calculation, that is, we know the area and we are asked to calculate the length of the segment $KP$.

In the first step, we replace the data we know in the kite area formula.

We obtain:

$A=(LN\times KM)$

$144=\frac{(18\times KM)}{2}$

**We simplify the expression and obtain:**

$288=18\times KM$

$KM=16$

**In fact, we found the length of the second diagonal of the kite.**

According to one of the properties of the kite, the diagonal $LN$ divides the diagonal $KP$ into two equal parts.

From here we obtain that $KP$ is equal to $8$ cm.

**Answer**:

$KP=8$ cm

Given kite ABCD AB=BC DC=AD

The diagonals of the kite intersect at point 0

Given BD=14 The area of the kite is 42 cm²

Calculate the side AO

We replace the data we have in the formula for the area of the kite:

Diagonal by diagonal divided by 2, we replace the existing data in the formula:

$S=\frac{AC\times BD}{2}$

$42=\frac{AC\times14}{2}$

We multiply by 2 to get rid of the denominator:

$14AC=84$

We divide by 14:

$AC=6$

Let's pay attention that we were asked about AO.

It is known that in a rhombus, the main diagonal crosses the second diagonal, therefore:

$AO=\frac{AC}{2}=\frac{6}{2}=3$

3 cm

Do you think you will be able to solve it?

Question 1

Given the deltoid ABCD

Find the area

Question 2

Given the deltoid ABCD

Find the area

Question 3

Given the deltoid ABCD

Find the area

Related Subjects

- Area of Equilateral Triangles
- Area of a Scalene Triangle
- Area of Isosceles Triangles
- Area of a right triangle
- Trapezoids
- Parallelogram
- Perimeter of a Parallelogram
- Kite
- The Area of a Rhombus
- Congruent Rectangles
- Acute triangle
- Obtuse Triangle
- Scalene triangle
- Triangle Height
- Exterior angle of a triangle
- Rhombus, kite, or diamond?
- Perimeter
- Triangle