Deltoid area - Examples, Exercises and Solutions

Look at the deltoid in the figure:

What is its area?

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

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 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

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

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?

It is not possible.

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.

Given the deltoid ABCD

Find the area

$20$ cm².

Given the deltoid ABCD

Find the area

$40$ cm².

Given the deltoid ABCD

Find the area

$45$ cm².

Given the deltoid ABCD

Find the area

$55$ cm².

Given the deltoid ABCD

Find the area

$47.5$ cm².

Indicate the correct answer

The next quadrilateral is:

Convex deltoid