Area of a Deltoid: Calculate The Missing Side based on the formula

The deltoid below has an area of 60 cm².

What is the value of X?

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

15

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

Given the deltoid ABCD

Side length BD equals 7 cm

The area of the deltoid is equal to 49 cm².

Find the length of the side AC

$14$ cm

Given the deltoid ABCD

Side length AC equals 10 cm

The area of the deltoid is equal to 40 cm².

Find the length of the side BD

$8$ cm

Given the deltoid ABCD

Side length BD equals 4 cm

The area of the deltoid is equal to 20 cm².

Find the length of the side AC

$10$ cm

Given the deltoid ABCD

Side length AC equals 13 cm

The area of the deltoid is equal to 39 cm².

Find the length of the side BD

$6$ cm

Given the deltoid ABCD

Side length BD equals 6 cm

The area of the deltoid is equal to 54 cm².

Find the length of the side AC

$18$ cm

Given the deltoid ABCD

Side length AC equals 11 cm

The area of the deltoid is equal to 44 cm².

Find the length of the side BD

$8$ cm

Given the deltoid ABCD

Side length AC equals 9 cm

The area of the deltoid is equal to 72 cm².

Find the length of the side BD

$16$ cm

Given ABCD deltoid AD=AB CB=CD

The diagonals of the deltoid intersect at the point O

Given in cm AO=6 BO=5

The area of the deltoid is equal to 80 cm².

Calculate the side CO

10

Given the deltoid ABCD

Side length BD equals 12 cm

The area of the deltoid is equal to 60 cm².

Find the length of the side AC

$10$ cm

Given the deltoid ABCD

Side length AC equals 8 cm

The area of the deltoid is equal to 64 cm².

Find the length of the side BD

$16$ cm

Given below is the deltoid ABCD.

Side length MD equals 3 cm.

The area of the deltoid is 72 cm².

What is the length of the side AC?

$24$ cm

Shown below is the deltoid ABCD.

Side length BM equals 2 cm.

The area of the deltoid is 72 cm².

Find the length of the side AC.

$36$ cm

Below is the deltoid ABCD.

Side length BD equals 15 cm.

The area of the deltoid is 60 cm².

Find the length of the side AC.

$8$ cm

Given the deltoid ABCD

Side length AC equal to 5.5 cm

The area of the deltoid is equal to 27.5 cm².

Find the length of the side BD

$10$ cm

The deltoid ABCD is shown below.

Side length AC equals 6 cm.

The area of the deltoid is 48 cm².

What is the length of the side BD?

$16$ cm

Look at the deltoid ABCD below.

DB = 9

The area of the deltoid is equal to 45 cm².

Calculate the length of side AC.

10 cm

Given the deltoid ABCD

DB=4 the area of the deltoid is equal to 32 cm².

Calculate the side AC

16 cm

Shown below is the deltoid ABCD.

DB = 4

The area of the deltoid is 28 cm².

Calculate the length of side AC.

14 cm²