## How do we calculate the area of a kite?

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

### Deltoid Area Formula

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

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

## Examples with solutions for Area of a Deltoid

### Exercise #1

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.

### Step-by-Step Solution

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide the product by 2.

We substitute the known data into the formula:

$\frac{8\cdot DB}{2}=32$

We reduce the 8 and the 2:

$4DB=32$

Divide by 4

$DB=8$

8 cm

### Exercise #2

ACBD is a deltoid.

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

### Step-by-Step Solution

To solve the exercise, we first need to remember how to calculate the area of a rhombus:

(diagonal * diagonal) divided by 2

Let's plug in the data we have from the question

10*6=60

60/2=30

And that's the solution!

30

### Exercise #3

Look at the deltoid in the figure:

What is its area?

### Step-by-Step Solution

Let's begin by reminding ourselves of the formula for the area of a kite

$\frac{Diagonal1\times Diagonal2}{2}$

Both these values are given to us in the figure thus we can insert them directly into the formula:

(4*7)/2

28/2

14

14

### Exercise #4

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

CB = 16

Calculate the area of the deltoid.

### Step-by-Step Solution

First, let's recall the formula for the area of a rhombus -

(Diagonal 1 * Diagonal 2) divided by 2

Let's substitute the known data into the formula:

(12*16)/2
192/2=
96

And that's the solution!

96 cm²

### Exercise #5

The kite ABCD shown below has an area of 42 cm².

AB = BC

BD = 14

The diagonals of the kite intersect at point 0.

Calculate the length of side AO.

### Step-by-Step Solution

We substitute the data we have into the formula for the area of the kite:

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

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

We multiply by 2 to remove the denominator:

$14AC=84$

Then divide by 14:

$AC=6$

In a rhombus, the main diagonal crosses the second diagonal, therefore:

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

3 cm

### Exercise #6

In a rectangular shopping mall they want to place a deltoid-shaped stage.

The length of the rectangle is 30 meters and the width 20 meters.

What is the area of the orange scenario?

### Step-by-Step Solution

We can calculate the area of rectangle ABCD:

$20\times30=600$

Let's divide the deltoid along its length and width and add the following points:

Now we can calculate the area of deltoid PMNK:

$PMNK=\frac{PN\times MK}{2}=\frac{20\times30}{2}=\frac{600}{2}=300$

300 m

Convex deltoid

Not deltoid

### Video Solution

It is not possible to prove if it is a deltoid or not

### Video Solution

It is not possible to prove if it is a deltoid or not

### Video Solution

It is not possible to prove if it is a deltoid or not

### Video Solution

It is not possible to prove if it is a deltoid or not

Not deltoid

Concave deltoid