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

\(\displaystyle \text{Area}=\text{base}\times\text{height}\)

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.

\(\displaystyle \sin x=\frac{\text{height}}{\text{side}}\), where \(\displaystyle x\) is the given angle.

\(\displaystyle \text{height}=(\text{side})(\sin x)\)

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

\(\displaystyle \text{Area}=(side)^2 \sin x\)

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

\(\displaystyle \text{Area}=(9)^2\sin 24=32.95\)

Make sure to round to \(\displaystyle 2\) places after the decimal.

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

\(\displaystyle \text{Area}=\text{base}\times\text{height}\)

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.

\(\displaystyle \sin x=\frac{\text{height}}{\text{side}}\), where \(\displaystyle x\) is the given angle.

\(\displaystyle \text{height}=(\text{side})(\sin x)\)

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

\(\displaystyle \text{Area}=(side)^2 \sin x\)

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

\(\displaystyle \text{Area}=(10)^2\sin 30=50\)

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

\(\displaystyle \text{Area}=\text{base}\times\text{height}\)

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.

\(\displaystyle \sin x=\frac{\text{height}}{\text{side}}\), where \(\displaystyle x\) is the given angle.

\(\displaystyle \text{height}=(\text{side})(\sin x)\)

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

\(\displaystyle \text{Area}=(side)^2 \sin x\)

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

\(\displaystyle \text{Area}=(16)^2\sin 58=217.10\)

Make sure to round to \(\displaystyle 2\) places after the decimal.

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

\(\displaystyle \text{Area}=\text{base}\times\text{height}\)

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.

\(\displaystyle \sin x=\frac{\text{height}}{\text{side}}\), where \(\displaystyle x\) is the given angle.

\(\displaystyle \text{height}=(\text{side})(\sin x)\)

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

\(\displaystyle \text{Area}=(side)^2 \sin x\)

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

\(\displaystyle \text{Area}=(24)^2\sin 95=573.81\)

Make sure to round to \(\displaystyle 2\) places after the decimal.

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

\(\displaystyle \text{Area}=\text{base}\times\text{height}\)

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.

\(\displaystyle \sin x=\frac{\text{height}}{\text{side}}\), where \(\displaystyle x\) is the given angle.

\(\displaystyle \text{height}=(\text{side})(\sin x)\)

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

\(\displaystyle \text{Area}=(side)^2 \sin x\)

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

\(\displaystyle \text{Area}=(2)^2\sin 104=3.88\)

Make sure to round to \(\displaystyle 2\) places after the decimal.

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

\(\displaystyle \text{Area}=\text{base}\times\text{height}\)

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.

\(\displaystyle \sin x=\frac{\text{height}}{\text{side}}\), where \(\displaystyle x\) is the given angle.

\(\displaystyle \text{height}=(\text{side})(\sin x)\)

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

\(\displaystyle \text{Area}=(side)^2 \sin x\)

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

\(\displaystyle \text{Area}=(3)^2\sin 112=8.34\)

Make sure to round to \(\displaystyle 2\) places after the decimal.

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

\(\displaystyle \text{Area}=\text{base}\times\text{height}\)

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.

\(\displaystyle \sin x=\frac{\text{height}}{\text{side}}\), where \(\displaystyle x\) is the given angle.

\(\displaystyle \text{height}=(\text{side})(\sin x)\)

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

\(\displaystyle \text{Area}=(side)^2 \sin x\)

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

\(\displaystyle \text{Area}=(7)^2\sin 129=38.08\)

Make sure to round to \(\displaystyle 2\) places after the decimal.

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

\(\displaystyle \text{Area}=\text{base}\times\text{height}\)

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.

\(\displaystyle \sin x=\frac{\text{height}}{\text{side}}\), where \(\displaystyle x\) is the given angle.

\(\displaystyle \text{height}=(\text{side})(\sin x)\)

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

\(\displaystyle \text{Area}=(side)^2 \sin x\)

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

\(\displaystyle \text{Area}=(9)^2\sin 84=80.56\)

Make sure to round to \(\displaystyle 2\) places after the decimal.

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

\(\displaystyle \text{Area}=\text{base}\times\text{height}\)

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.

\(\displaystyle \sin x=\frac{\text{height}}{\text{side}}\), where \(\displaystyle x\) is the given angle.

\(\displaystyle \text{height}=(\text{side})(\sin x)\)

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

\(\displaystyle \text{Area}=(side)^2 \sin x\)

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

\(\displaystyle \text{Area}=(4)^2\sin 82=15.84\)

Make sure to round to \(\displaystyle 2\) places after the decimal.

To find the value of diagonal \(\displaystyle \small \overline{FH}\), we must first recognize some important properties of rhombuses. Since the perimeter is of \(\displaystyle \small EFGH\) is \(\displaystyle \small 24\), and by definition a rhombus has four sides of equal length, each side length of the rhombus is equal to \(\displaystyle \small 6\). The diagonals of rhombuses also form four right triangles, with hypotenuses equal to the side length of the rhombus and legs equal to one-half the lengths of the diagonals. We can therefore use the Pythagorean Theorem to solve for one-half of the unknown diagonal:

\(\displaystyle \small 6^2=5^2+x^2\), where \(\displaystyle \small 6\) is the rhombus side length, \(\displaystyle \small 5\) is one-half of the known diagonal, and \(\displaystyle \small x\) is one-half of the unknown diagonal. We can therefore solve for \(\displaystyle \small x\):

\(\displaystyle \small x^2=6^2-5^2=36-25=11\)

\(\displaystyle \small x\) is therefore equal to \(\displaystyle \small \sqrt{11}\). Since \(\displaystyle \small x\) represents one-half of the unknown diagonal, we need to multiply by \(\displaystyle \small 2\) to find the full length of diagonal \(\displaystyle \small \overline{FH}\).

The length of diagonal \(\displaystyle \small \overline{FH}\) is therefore \(\displaystyle \small 2\sqrt{11}\)