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Advanced Geometry : How to find the area of a rhombus

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Example Question #121 : Plane Geometry

Find the area of the rhombus.

Possible Answers:

8.34

9.05

8.08

7.18

Correct answer:

8.34

Explanation:

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

$\text{Area}=\text{base}\times\text{height}$

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.

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

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

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

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

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

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

Make sure to round to places after the decimal.

Report an Error

Example Question #41 : Rhombuses

Find the area of the rhombus.

Possible Answers:

29.47

31.56

38.08

28.88

Correct answer:

38.08

Explanation:

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

$\text{Area}=\text{base}\times\text{height}$

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.

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

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

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

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

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

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

Make sure to round to places after the decimal.

Report an Error

Example Question #121 : Plane Geometry

Find the area of the rhombus.

Possible Answers:

80.56

82.52

82.51

79.65

Correct answer:

80.56

Explanation:

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

$\text{Area}=\text{base}\times\text{height}$

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.

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

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

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

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

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

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

Make sure to round to places after the decimal.

Report an Error

Example Question #41 : Rhombuses

Find the area of the rhombus.

Possible Answers:

17.26

19.02

15.84

16.51

Correct answer:

15.84

Explanation:

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

$\text{Area}=\text{base}\times\text{height}$

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.

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

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

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

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

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

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

Make sure to round to places after the decimal.

Report an Error

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Advanced Geometry : How to find the area of a rhombus

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #121 : Plane Geometry

Example Question #41 : Rhombuses

Example Question #121 : Plane Geometry

Example Question #41 : Rhombuses

All Advanced Geometry Resources

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