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

## Example Questions

### Example Question #31 : How To Find The Area Of A Rhombus

Find the area of the rhombus below.

Explanation:

Recall that the diagonals of the rhombus are perpendicular bisectors. From the given side and the given diagonal, we can find the length of the second diagonal by using the Pythagorean Theorem.

Let the given diagonal be diagonal 1, and rearrange the equation to solve for diagonal 2.

Plug in the given side and diagonal to find the length of diagonal 2.

Now, recall how to find the area of a rhombus:

Plug in the two diagonals to find the area.

Make sure to round to  places after the decimal.

### Example Question #31 : Rhombuses

A rhombus is  meters across.   .  Find the area.

m2

Explanation:

1) Substitute  into the expression .

2) Substitute  and  into the rhombus area formula,

### Example Question #413 : Advanced Geometry

Find the area of the rhombus.

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

, where  is the given angle.

Now, plug this into the equation for the area to get the following equation:

Plug in the given side length and angle values to find the area.

Make sure to round to  places after the decimal.

### Example Question #414 : Advanced Geometry

Find the area of the rhombus.

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

, where  is the given angle.

Now, plug this into the equation for the area to get the following equation:

Plug in the given side length and angle values to find the area.

Make sure to round to  places after the decimal.

### Example Question #415 : Advanced Geometry

Find the area of the rhombus.

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

, where  is the given angle.

Now, plug this into the equation for the area to get the following equation:

Plug in the given side length and angle values to find the area.

Make sure to round to  places after the decimal.

### Example Question #32 : Rhombuses

Find the area of the rhombus.

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

, where  is the given angle.

Now, plug this into the equation for the area to get the following equation:

Plug in the given side length and angle values to find the area.

Make sure to round to  places after the decimal.

### Example Question #33 : Rhombuses

Find the area of the rhombus.

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

, where  is the given angle.

Now, plug this into the equation for the area to get the following equation:

Plug in the given side length and angle values to find the area.

### Example Question #34 : Rhombuses

Find the area of the rhombus.

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

, where  is the given angle.

Now, plug this into the equation for the area to get the following equation:

Plug in the given side length and angle values to find the area.

Make sure to round to  places after the decimal.

### Example Question #35 : Rhombuses

Find the area of the rhombus.

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

, where  is the given angle.

Now, plug this into the equation for the area to get the following equation:

Plug in the given side length and angle values to find the area.

Make sure to round to  places after the decimal.

### Example Question #36 : Rhombuses

Find the area of the rhombus.

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

, where  is the given angle.

Now, plug this into the equation for the area to get the following equation:

Plug in the given side length and angle values to find the area.

Make sure to round to  places after the decimal.