Area of a Deltoid: Applying the formula

Look at the deltoid in the figure:

What is its area?

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

15

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

Given the deltoid ABCD

Find the area

$12$ cm².

Given the deltoid ABCD

Find the area

$17.5$ cm².

Given the deltoid ABCD

Find the area

$27$ cm².

Given the deltoid ABCD

Find the area

$35$cm².

Given the deltoid ABCD

Find the area

$36$ cm².

Look at the deltoid ABCD below.

Diagonal DB = 4

The area of the deltoid is 24 cm².

Calculate the diagonal AC.

12 cm

Shown below is the deltoid ABCD.

The diagonal AC is 3 cm long.

The area of the deltoid is 18 cm².

Calculate the diagonal DB.

12 cm

Look at the deltoid ABCD below.

Given in cm:

AC = 7

DB = 5

Calculate the area of the deltoid.

17.5 cm².

Given the deltoid ABCD

Find the area

$22.5$ cm².

Given the deltoid ABCD

Find the area

$113.75$ cm².

Given the deltoid ABCD

Find the area

$20$ cm².

Given the deltoid ABCD

Find the area

$67.5$ cm².

Given the deltoid ABCD

Find the area

$44$ cm².