Advanced Geometry : Plane Geometry

Study concepts, example questions & explanations for Advanced Geometry

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Example Questions

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

Find the area of the rhombus.

2

Possible Answers:

\(\displaystyle 25.08\)

\(\displaystyle 27.64\)

\(\displaystyle 32.79\)

\(\displaystyle 31.24\)

Correct answer:

\(\displaystyle 32.79\)

Explanation:

13

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.

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

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

 

Example Question #121 : Quadrilaterals

Find the area of the rhombus.

3

Possible Answers:

\(\displaystyle 38.56\)

\(\displaystyle 45.12\)

\(\displaystyle 31.24\)

\(\displaystyle 39.40\)

Correct answer:

\(\displaystyle 39.40\)

Explanation:

13

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.

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

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

 

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

Find the area of the rhombus.

4

Possible Answers:

\(\displaystyle 39.78\)

\(\displaystyle 31.93\)

\(\displaystyle 32.95\)

\(\displaystyle 40.51\)

Correct answer:

\(\displaystyle 32.95\)

Explanation:

13

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.

 

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

Find the area of the rhombus.

5

Possible Answers:

\(\displaystyle 63.21\)

\(\displaystyle 52.19\)

\(\displaystyle 45\)

\(\displaystyle 50\)

Correct answer:

\(\displaystyle 50\)

Explanation:

13

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.

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

 

Example Question #31 : Rhombuses

Find the area of the rhombus.

6

Possible Answers:

\(\displaystyle 213.49\)

\(\displaystyle 217.10\)

\(\displaystyle 227.61\)

\(\displaystyle 205.41\)

Correct answer:

\(\displaystyle 217.10\)

Explanation:

13

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.

 

Example Question #31 : Rhombuses

Find the area of the rhombus.

7

Possible Answers:

\(\displaystyle 500.24\)

\(\displaystyle 573.81\)

\(\displaystyle 551.68\)

\(\displaystyle 495.81\)

Correct answer:

\(\displaystyle 573.81\)

Explanation:

13

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.

 

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

Find the area of the rhombus.

8

Possible Answers:

\(\displaystyle 2.91\)

\(\displaystyle 3.88\)

\(\displaystyle 3.49\)

\(\displaystyle 5.37\)

Correct answer:

\(\displaystyle 3.88\)

Explanation:

13

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.

 

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

Find the area of the rhombus.

9

Possible Answers:

\(\displaystyle 8.34\)

\(\displaystyle 8.08\)

\(\displaystyle 7.18\)

\(\displaystyle 9.05\)

Correct answer:

\(\displaystyle 8.34\)

Explanation:

13

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.

 

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

Find the area of the rhombus.

10

Possible Answers:

\(\displaystyle 28.88\)

\(\displaystyle 29.47\)

\(\displaystyle 31.56\)

\(\displaystyle 38.08\)

Correct answer:

\(\displaystyle 38.08\)

Explanation:

13

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.

 

Example Question #41 : Rhombuses

Find the area of the rhombus.

11

Possible Answers:

\(\displaystyle 82.51\)

\(\displaystyle 82.52\)

\(\displaystyle 80.56\)

\(\displaystyle 79.65\)

Correct answer:

\(\displaystyle 80.56\)

Explanation:

13

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.

 

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