### All High School Math Resources

## Example Questions

### Example Question #1 : How To Find If Rhombuses Are Similar

A quadrilateral ABCD has diagonals that are perpendicular bisectors of one another. Which of the following classifications must apply to quadrilateral ABCD?

I. parallelogram

II. rhombus

III. square

**Possible Answers:**

I, II, and III

I and III only

I and II only

II and III only

**Correct answer:**

I and II only

If the diagonals of a quadrilateral are perpendicular bisectors of one another, then the quadrilateral must be a rhombus, but not necessarily a square. Since all rhombi are also parallelograms, quadrilateral ABCD must be both a rhombus and parallelogram.

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

This figure is a rhombus with a side of 8 in.

What is the area of the rhombus (in^{2})?

**Possible Answers:**

Not enough information

**Correct answer:**

Not enough information

In order to determine the area of a rhombus you either need a base and a height OR the length of the two diagonals OR the base and an angle. Because we are only given the base with no information about the height, there is not enough information to determine the area of the rhombus.

### Example Question #2 : How To Find The Area Of A Rhombus

Find the area of the following rhombus:

The perimeter of the rhombus is .

**Possible Answers:**

**Correct answer:**

The formula for the perimeter of a rhombus is:

Where is the length of the side

Plugging in our values, we get:

The formula for the area of a rhombus is:

Where is the length of one diagonal and is the length of another diagonal

By drawing the diagonals, we create a right triangle with the hypotenuse as and the side as .

Since we know that is a phythagorean triple, we can infer that the third side is .

Plugging in our values, we get:

### Example Question #1 : Rhombuses

This figure is a rhombus with a side of 8 in.

What is the perimeter of the rhombus (in)?

**Possible Answers:**

**Correct answer:**

The perimeter of the rhombus is the distance around the outside of the figure. Since a rhombus has 4 congruent sides, the perimeter is simply .

### Example Question #2 : Rhombuses

You are given a rhombus with a side of meters. What is the perimeter of the rhombus?

**Possible Answers:**

meters

meters

meters

meters

meters

**Correct answer:**

meters

A rhombus is a quadrilateral ( sided figure) with congruent sides. The perimeter is the sum of the sides. Thus, to find the perimeter of the rhombus, we multiply the perimeter by . This gives us meters.

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