# ISEE Upper Level Math : Rhombuses

## Example Questions

### Example Question #1 : How To Find The Area Of A Rhombus

Two diagonals of a rhombus have lengths of  and . Give the area in terms of .

Explanation:

The formula for the area of a rhombus is

,

where is the length of one diagonal and is the length of the other diagonal.

### Example Question #1 : Rhombuses

A rhombus has side length , and one of the interior angles is . Give the area of the rhombus.

Explanation:

The area of a rhombus can be determined by the following formula:

,

where is the length of any side and is any interior angle.

### Example Question #3 : How To Find The Area Of A Rhombus

Find the area of a rhombus with one diagonal having a length of 12in and the other having a length two times the first diagonal.

Explanation:

To find the area of a rhombus, we will use the following formula:

where p and q are the lengths of the diagonals of the rhombus.

Now, we know one diagonal has a length of 12in.  We also know the other diagonal is two times the first diagonal.  Therefore, the second diagonal is 24in.

Knowing this, we can substitute into the formula.  We get

### Example Question #1 : How To Find The Length Of The Side Of A Rhombus

A rhombus has a perimeter of . Give the side length of the rhombus.

Explanation:

Like any polygon, the perimeter of the rhombus is the total distance around the outside, which can be found by adding together the length of each side. In the case of a rhombus, all four sides have the same length, i.e.

,

where is the length of each side.

### Example Question #1 : How To Find The Length Of The Side Of A Rhombus

A rhombus has the area of . One of the interior angles is . Give the length of each side of the rhombus.

Explanation:

The area of a rhombus can be determined by the following formula:

,

where is the length of any side and is any interior angle.

### Example Question #1 : How To Find The Perimeter Of A Rhombus

One side of a rhombus measures 2 yards. Which of the following is equal to the perimeter?

All of the other choices give the correct perimeter.

Explanation:

A rhombus has four sides of equal measure, so the perimeter of a rhombus with sidelength 2 yards is  yards.

Also,

The only choice that agrees with any of these measures is 288 inches, the correct choice.

### Example Question #1 : Rhombuses

One side of a rhombus measures . Give its perimeter in terms of .

Explanation:

A rhombus has four sides of equal measure, so the perimeter of a rhombus with sidelength  is .

### Example Question #1 : How To Find An Angle In A Rhombus

Consider the rhombus below. Solve for .

Explanation:

The total sum of the interior angles of a quadrilateral is  degrees. In this problem, we are only considering half of the interior angles:

### Example Question #1 : How To Find An Angle In A Rhombus

Note: Figure NOT drawn to scale.

The above depicts a rhombus and one of its diagonals. What is ?