You will learn here to find the area of a rhombus when the lengths of the diagonals are not given explicitly. You will need to use a property of the rhombus and knowledge that you have about Pythagorean triples.

**Example**

Use the rhombus ABCD below in order to find the area of the rhombus.

The formula to use to find the area of a rhombus is area = 0.5(d_{1}× d_{2}), where d_{1} and d_{2} are the lengths of the diagonals.

Notice that d_{1} could be, for example, the length of AC and d_{2} could be the length of DB.

Notice also that EB is equal to 8. Furthermore, we know that the diagonals of a rhombus bisect each other. This means that segment AC bisects DB. We can then conclude that DE is also equal to 8. Therefore, DB = DE + EB = 8 + 8 = **16**.

Now we need to find the length of AC.

Since AC is a perpendicular bisector, triangle ABE is a right triangle with AB = 10 and EB = 8.

(3, 4, 5) is a Pythagorean triple. If we multiply each number by 2, we get another Pythagorean triple or (6, 8, 10).

8 and 10 are parts of a Pythagorean triple whose missing third number is 6.

Therefore, using a Pythagorean triple, AE is equal to 6.

Lastly, BD bisects AC. We can then conclude that EC is also equal to 6.

Therefore, AC = AE + EC = 6 + 6 = **12**.

d_{1} = AC = 12 and d_{2} = DB = 16

Area = 0.5(d_{1}× d_{2})

Area = 0.5(12 × 16)

Area = 0.5(192)

Area = 96