# Advanced Geometry : How to find the area of a rhombus

## Example Questions

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

Which of the following shapes is a rhombus?

Explanation:

A rhombus is a four-sided figure where all sides are straight and equal in length. All opposite sides are parallel. A square is considered to be a rhombus.

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

Assume quadrilateral  is a rhombus. If diagonal  and diagonal , what is the area of rhombus

Explanation:

Solving for the area of rhombus  requires knowledge of the equation for finding the area of a rhombus. The equation is , where  and  are the two diagonals of the rhombus. Since both of these values are given to us in the original problem, we merely need to substitute these values into the equation to obtain:

The area of rhombus  is therefore  square units.

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

What is the area of the rhombus above?

Explanation:

The formula for the area of a rhombus from the diagonals is half the product of the diagonals, or in mathematical terms:

where  and  are the lengths of the diagonals.

Substituting our values yields,

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

Above is a rhombus imposed on a rectangle. What is the area of the rhombus?

Explanation:

One of the formulas for a rhombus is base times height,

Since a rhombas has equal sides, the base is 5 and the height of the rhombus is the same as the height of the rectangle, 4.

Substituting in these values we get the following:

### Example Question #5 : Rhombuses

Assume quadrilateral  is a rhombus. The perimeter of  is , and the length of one of its diagonals is . What is the area of ?

Explanation:

To solve for the area of the rhombus , we must use the equation , where  and  are the diagonals of the rhombus. Since the perimeter of the rhombus is , and by definition all 4 sides of a rhombus have the same length, we know that the length of each side is . We can find the length of the other diagonal if we recognize that the two diagonals combined with a side edge form a right triangle. The length of the hypotenuse is , and each leg of the triangle is equal to one-half of each diagonal. We can therefore set up an equation involving Pythagorean's Theorem as follows:

, where  is equal to one-half the length of the unknown diagonal.

We can therefore solve for  as follows:

is therefore equal to 8, and our other diagonal is 16. We can now use both diagonals to solve for the area of the rhombus:

The area of rhombus  is therefore equal to

### Example Question #5 : How To Find The Area Of A Rhombus

What is the area of a rhombus with diagonal lengths of  and ?

Explanation:

The area of a rhombus is given below. Plug in the diagonals and solve for the area.

### Example Question #6 : How To Find The Area Of A Rhombus

Find the area of a rhombus if the diagonal lengths are  and .

Explanation:

The area of the rhombus is given below.  Substitute the diagonals into the formula.

### Example Question #4 : How To Find The Area Of A Rhombus

Find the area of a rhombus if its diagonal lengths are and .

Explanation:

Write the equation for the area of a rhombus.

Substitute the diagonals and evaluate the area.

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

Find the area of a rhombus if the both diagonals have a length of .

Explanation:

Write the formula for the area of a rhombus.

Since both diagonals are equal, .  Plug in the diagonals and reduce.

### Example Question #10 : Rhombuses

What is the area of a rhombus if the diagonals are  and ?

Explanation:

Write the formula for an area of a rhombus.

Substitute the diagonal lengths provided into the formula.

Multiply the two terms in the numerator.

You can consider the outermost division by two as multiplying everything in the numerator by .

Multiply across and reduce to arrive at the correct answer.

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