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 2 isosceles triangles that share a common base.

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

A quadrilateral that has 2 pairs of equal adjacent sides

Example:

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

Then: ABCD 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° 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.
A1 - Deltoid

Practice Deltoid

Exercise #1

Look at the deltoid in the figure:

777444

What is its area?

Video Solution

Step-by-Step Solution

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

Diagonal1×Diagonal22 \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

Answer

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.

S=32S=32S=32888AAABBBCCCDDD

Video Solution

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:

 8DB2=32 \frac{8\cdot DB}{2}=32

We will reduce the 8 and the 2:

4DB=32 4DB=32

Divide by 4

DB=8 DB=8

Answer

8 cm

Exercise #3

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

AB = BC

DC = AD

BD = 14

The diagonals of the kite intersect at point 0.

Calculate the length of side AO.

S=42S=42S=42141414DDDAAABBBCCCOOO

Video Solution

Step-by-Step Solution

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

S=AC×BD2 S=\frac{AC\times BD}{2}

42=AC×142 42=\frac{AC\times14}{2}

We multiply by 2 to remove the denominator:

 14AC=84 14AC=84

Then divide by 14:

AC=6 AC=6

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

AO=AC2=62=3 AO=\frac{AC}{2}=\frac{6}{2}=3

Answer

3 cm

Exercise #4

Look at the deltoid in the figure:

555666

What is its area?

Video Solution

Answer

15

Exercise #5

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

666101010AAACCCBBBDDD

Video Solution

Answer

30

Exercise #1

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

AD = 12

CB = 16

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

Video Solution

Answer

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?

444101010AAADDDCCCBBB

Video Solution

Answer

It is not possible.

Exercise #3

Given the deltoid ABCD

Find the area

666444AAABBBCCCDDD

Video Solution

Answer

12 12 cm².

Exercise #4

Given the deltoid ABCD

Find the area

777555AAABBBCCCDDD

Video Solution

Answer

17.5 17.5 cm².

Exercise #5

Given the deltoid ABCD

Find the area

999666AAADDDCCCBBB

Video Solution

Answer

27 27 cm².

Exercise #1

Given the deltoid ABCD

Find the area

101010777CCCBBBAAADDD

Video Solution

Answer

35 35 cm².

Exercise #2

Given the deltoid ABCD

Find the area

999888AAADDDCCCBBB

Video Solution

Answer

36 36 cm².

Exercise #3

Given the deltoid ABCD

Find the area

555888AAADDDCCCBBB

Video Solution

Answer

20 20 cm².

Exercise #4

Given the deltoid ABCD

Find the area

555161616AAADDDCCCBBB

Video Solution

Answer

40 40 cm².

Exercise #5

Given the deltoid ABCD

Find the area

555181818AAADDDCCCBBB

Video Solution

Answer

45 45 cm².