The perimeter of a rhombus is 40. What is the area of the square?

96 cm squared

Step-by-step explanation:

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

40cm

4 = 10cm

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

12cm

2 = 6cm

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

√ (10cm) squared - (6cm) squared = 8cm

Now find the area of the triangle.

1

2 * 6cm * 8cm = 24cm squared

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

24cm squared * 4 = 96cm squared