# 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?

##### 1 Answer

Mar 27, 2017

#### 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.

#1/2 xx 6 "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 "cm"^2 xx 4 = 96 "cm"^2#