# Deltoid - Examples, Exercises and Solutions

## The Deltoid and Everything You Need to Know to Verify It

### What is a Kite or Deltoid?

In geometry, a deltoid is defined as a quadrilateral consisting of $2$ isosceles triangles that share a common base.

#### So, what is the identification of a deltoid in the family of quadrilaterals?

Example:

If given : $AD=AB,DC=BC$

Then: $ABCD$ is a deltoid by definition.

• 2 isosceles triangles with a common base form a deltoid.
• The sum of the angles in the deltoid is $360°$ degrees.
• The area of the deltoid contains the number of quadrilaterals that cover the selected parts of the plane.
• The perimeter of the deltoid is the length of the thread with which we border the outline of the deltoid and is measured in units of length in meters or cm.

## Practice Deltoid

### Exercise #1

Look at the deltoid in the figure:

What is its area?

### Step-by-Step Solution

Initially, let's remember the formula for the area of a kite

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

Both pieces of information already exist, so we can place them in the formula:

(4*7)/2

28/2

14

14

### Exercise #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.

### 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 this product by 2.

We substitute the known data into the formula:

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

We will reduce the 8 and the 2:

$4DB=32$

Divide by 4

$DB=8$

8 cm

### Exercise #3

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 #4

Look at the deltoid in the figure:

What is its area?

15

### Exercise #5

ACBD is a deltoid.

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

30

### Exercise #1

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

CB = 16

Calculate the area of the deltoid.

96 cm²

### Exercise #2

Look at the kite ABCD below.

Diagonal DB = 10

CB = 4

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

### Video Solution

It is not possible.

### Exercise #3

Given the deltoid ABCD

Find the area

### Video Solution

$12$ cm².

### Exercise #4

Given the deltoid ABCD

Find the area

### Video Solution

$17.5$ cm².

### Exercise #5

Given the deltoid ABCD

Find the area

### Video Solution

$27$ cm².

### Exercise #1

Given the deltoid ABCD

Find the area

### Video Solution

$35$cm².

### Exercise #2

Given the deltoid ABCD

Find the area

### Video Solution

$36$ cm².

### Exercise #3

Given the deltoid ABCD

Find the area

### Video Solution

$20$ cm².

### Exercise #4

Given the deltoid ABCD

Find the area

### Video Solution

$40$ cm².

### Exercise #5

Given the deltoid ABCD

Find the area

### Video Solution

$45$ cm².