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.
3 - Convex Kite

Practice Deltoid

Examples with solutions for Deltoid

Exercise #1

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

666101010AAACCCBBBDDD

Video Solution

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!

Answer

30

Exercise #2

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

AD = 12

CB = 16

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

Video Solution

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!

Answer

96 cm²

Exercise #3

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 the product by 2.

We substitute the known data into the formula:

 8DB2=32 \frac{8\cdot DB}{2}=32

We reduce the 8 and the 2:

4DB=32 4DB=32

Divide by 4

DB=8 DB=8

Answer

8 cm

Exercise #4

Look at the deltoid in the figure:

555666

What is its area?

Video Solution

Step-by-Step Solution

To solve the exercise, we need to know the formula for calculating the area of a kite:

It's also important to know that a concave kite, like the one in the question, has one of its diagonals outside the shape - but it's still its diagonal.

Let's plug the data from the question into the formula:

(6*5)/2=
30/2=
15

Answer

15

Exercise #5

Look at the deltoid in the figure:

777444

What is its area?

Video Solution

Step-by-Step Solution

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

Diagonal1×Diagonal22 \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

Answer

14

Exercise #6

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 #7

The deltoid below has an area of 60 cm².

888XXX

What is the value of X?

Video Solution

Step-by-Step Solution

To solve the problem, we need to remember the formula for the area of a rhombus:

The product of the diagonals multiplied together and divided by 2.

Let's plug in the data we have into the formula:

(8*X)=60
2

Note that we can simplify the fraction, thus eliminating the denominator:

4X=60

Let's divide the equation by 4

X=15

Answer

15

Exercise #8

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?

202020303030AAABBBCCCDDD

Video Solution

Step-by-Step Solution

We can calculate the area of rectangle ABCD:

20×30=600 20\times30=600

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

202020303030PPPMMMNNNKKKAAABBBCCCDDDNow we can calculate the area of deltoid PMNK:

PMNK=PN×MK2=20×302=6002=300 PMNK=\frac{PN\times MK}{2}=\frac{20\times30}{2}=\frac{600}{2}=300

Answer

300 m

Exercise #9

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 #10

Given the deltoid ABCD

Find the area

999666AAADDDCCCBBB

Video Solution

Answer

27 27 cm².

Exercise #11

Given the deltoid ABCD

Find the area

101010777CCCBBBAAADDD

Video Solution

Answer

35 35 cm².

Exercise #12

Given the deltoid ABCD

Find the area

999888AAADDDCCCBBB

Video Solution

Answer

36 36 cm².

Exercise #13

Given the deltoid ABCD

Find the area

555888AAADDDCCCBBB

Video Solution

Answer

20 20 cm².

Exercise #14

Given the deltoid ABCD

Find the area

555161616AAADDDCCCBBB

Video Solution

Answer

40 40 cm².

Exercise #15

Given the deltoid ABCD

Find the area

555181818AAADDDCCCBBB

Video Solution

Answer

45 45 cm².