A Guide to the GRE/Rhombuses

= Rhombuses =

Rules
The area of a rhombus or parallelogram is base multiplied by height.

The area of a rhombus is the product of its diagonals, which are perpendicular.

In this figure, the area is 8(6) or 	48.

The area of the figure to the left 	is 10(12) or 120.

In a rhombus or parallelogram, opposite angles are equal, and adjacent angles add up to 180º.

This follows from the rules of parallel lines and opposing and adjacent angles.

Practice
1. In the rhombus to the right, the distance from F to H is 10. If the area of the rhombus is 85, what is the distance from G to I

2. A rhombus has a perimeter of 60 and a diagonal of 18. What is its area?

Answers to Practice Questions
1. 8.5

The area of a rhombus is equal to the product of its diagonals. Since this rhombus has an area of 85 and a diagonal of 10, the second diagonal is equal toor 8.5.

2. 432

The diagonals of a rhombus are perpendicular, and its four sides are equal. Thus, a rhombus with a perimeter of 60 has sides of 15; if this rhombus has a diagonal of 18, it can be broken into right triangles. The third side of these triangles is equal to or 12. Thus, the diagonal is equal to 24 and thus its area is 432.