# The perimeter of a rhombus is 40 centimeters. The length of one diagonal is 12 centimeters. How do you find the area of the rhombus?

Mar 27, 2017

$96 {\text{cm}}^{2}$

#### Explanation:

A rhombus has 4 edges of equal length. If it has perimeter of 40cm, then each length would be

{40"cm"}/4 = 10"cm"

Divide the rhombus into 4 right-angle triangle by cutting along the 2 diagonals.

Each right-angle triangle will have a hypotenuse of 10cm and one other edge with length

{12"cm"}/2 = 6"cm"

Use Pythagoras Theorem to find the length of the remaining edge.

sqrt{(10"cm")^2 - (6"cm")^2} = 8 "cm"

Now find the area of the triangle.

$\frac{1}{2} \times 6 {\text{cm" xx 8"cm" = 24 "cm}}^{2}$

Since the original rhombus was made up of four such triangles, the area of the rhombus would be

$24 {\text{cm"^2 xx 4 = 96 "cm}}^{2}$