Area of a Deltoid - Examples, Exercises and Solutions

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.

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

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

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

Look at the deltoid in the figure:

What is its area?

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

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

AD = 12

CB = 16

Calculate the area of the deltoid.

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

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.

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

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?

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

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The next quadrilateral is:

Convex deltoid

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The next quadrilateral is:

Not deltoid

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The next quadrilateral is:

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

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The next quadrilateral is:

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

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The next quadrilateral is:

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

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The next quadrilateral is:

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

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The next quadrilateral is:

Not deltoid

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The next quadrilateral is:

Concave deltoid

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The next quadrilateral is:

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