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Advanced Geometry : Plane Geometry

Study concepts, example questions & explanations for Advanced Geometry

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6 Diagnostic Tests 57 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #34 : Rhombuses

Find the area of the rhombus.

Possible Answers:

27.64

32.79

25.08

31.24

Correct answer:

32.79

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.

$\text{Area}=(7)^2\sin 42=32.79$

Make sure to round to places after the decimal.

Report an Error

Example Question #35 : Rhombuses

Find the area of the rhombus.

Possible Answers:

45.12

38.56

31.24

39.40

Correct answer:

39.40

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.

$\text{Area}=(8)^2\sin 38=39.40$

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:

32.95

40.51

31.93

39.78

Correct answer:

32.95

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.

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

Make sure to round to places after the decimal.

Report an Error

Example Question #37 : Rhombuses

Find the area of the rhombus.

Possible Answers:

52.19

63.21

Correct answer:

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.

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

Report an Error

Example Question #38 : Rhombuses

Find the area of the rhombus.

Possible Answers:

205.41

227.61

213.49

217.10

Correct answer:

217.10

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.

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

Make sure to round to places after the decimal.

Report an Error

Example Question #39 : Rhombuses

Find the area of the rhombus.

Possible Answers:

551.68

495.81

573.81

500.24

Correct answer:

573.81

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.

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

Make sure to round to places after the decimal.

Report an Error

Example Question #40 : Rhombuses

Find the area of the rhombus.

Possible Answers:

3.88

3.49

2.91

5.37

Correct answer:

3.88

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.

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

Make sure to round to places after the decimal.

Report an Error

Example Question #41 : How To Find The Area Of A Rhombus

Find the area of the rhombus.

Possible Answers:

8.08

8.34

7.18

9.05

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:

38.08

28.88

31.56

29.47

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 #43 : How To Find The Area Of A Rhombus

Find the area of the rhombus.

Possible Answers:

80.56

82.51

82.52

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

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Advanced Geometry : Plane Geometry

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #34 : Rhombuses

Example Question #35 : Rhombuses

Example Question #121 : Plane Geometry

Example Question #37 : Rhombuses

Example Question #38 : Rhombuses

Example Question #39 : Rhombuses

Example Question #40 : Rhombuses

Example Question #41 : How To Find The Area Of A Rhombus

Example Question #41 : Rhombuses

Example Question #43 : How To Find The Area Of A Rhombus

All Advanced Geometry Resources

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