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Advanced Geometry : Advanced 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 #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.

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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.

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

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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:

9.05

8.08

8.34

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:

31.56

28.88

38.08

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

Example Question #131 : Plane Geometry

Find the area of the rhombus.

Possible Answers:

16.51

17.26

15.84

19.02

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

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

Assume quadrilateral $\small EFGH$ is a rhombus. If the perimeter of $\small EFGH$ is $\small 24$ and the length of diagonal $\small \overline{EG}=10$ , what is the length of diagonal $\small \overline{FH}$ ?

Possible Answers:

$\small 2\sqrt{5}$

$\small 2\sqrt{11}$

$\small \sqrt{11}$

$\small 5$

$\small 11$

Correct answer:

$\small 2\sqrt{11}$

Explanation:

To find the value of diagonal $\small \overline{FH}$ , we must first recognize some important properties of rhombuses. Since the perimeter is of $\small EFGH$ is $\small 24$ , and by definition a rhombus has four sides of equal length, each side length of the rhombus is equal to $\small 6$ . 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:

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

$\small x^2=6^2-5^2=36-25=11$

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

The length of diagonal $\small \overline{FH}$ is therefore $\small 2\sqrt{11}$

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Advanced Geometry : Advanced Geometry

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

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

Example Question #131 : Plane Geometry

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

All Advanced Geometry Resources

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