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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Parallelogram_custom_4

Find the perimeter of the parallelogram shown above.

Possible Answers:

$\small p=2(\sqrt{40})$

$\small p=\small 63$

$\small p=2(9+\sqrt{40})$

$\small p=(9+\sqrt{40})$

Correct answer:

$\small p=2(9+\sqrt{40})$

Explanation:

To solve this problem, apply the formula $\small \small perimeter=2(base+side)$ .

Since the length of the side is not provided in the figure, apply the formula $\small a^2 +b^2=c^2$ , where $\small a=h$ , $\small b=2$ and $\small c=$ the side of the parallelogram.

The solution is:

$\small 6^2+2^2=c^2$
$\small 36+4=c^2$
$\small 40=c^2$
$\small c=\sqrt{40}$

Thus,

$\small p=2(9+\sqrt{40})$

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Example Question #2 : How To Find The Perimeter Of A Parallelogram

A parallelogram has a base that is $\small 5$ times greater than the length of the side of the parallelogram. If the length of the side is $\small \small \sqrt{169}$ , what is the perimeter of the parallelogram?

Possible Answers:

$\small 65$

$\small 78$

$\small 165$

$\small 156$

Correct answer:

$\small 156$

Explanation:

To solve this problem, first find the $\small \sqrt{169}=13$ . Then to find the length of the base: $\small 13\times 5=65$

Then apply the formula:

$\small p=2(base+side)$ .

$\small p=2(65+13)$

$\small \small p=2(78)=156$

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Example Question #1 : How To Find The Perimeter Of A Parallelogram

Find the perimeter (in inches) of a parallelogram that has a base of $\small \small 1\frac{3}{4} ft$ and a side length of $\small 1\frac{1}{2} ft$ .

Possible Answers:

$\small 89in$

$\small 378 in$

$\small 78in$

$\small 39in$

Correct answer:

$\small 78in$

Explanation:

To find the perimeter of the parallelogram apply the formula: $\small Perimeter=2(base+side)$ . However, to find the solution with the correct unit, convert $\small 1\frac{3}{4} feet=21 inches$ and $\small 1\frac{1}{2}feet=18 inches$ . We can convert feet into inches because 12in=1ft .

Thus, the solution is:

$\small P=2(21+18)$
$\small P=2(39)$
$\small P=78$

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Example Question #1 : How To Find The Perimeter Of A Parallelogram

A parallelogram has a base length of $\small 15$ and a side length of $\small \frac{base}{2}$ . Find the perimeter of the parallelogram.

Possible Answers:

$\small 54$

$\small 30$

$\small 45$

$\small 39$

Correct answer:

$\small 45$

Explanation:

To solve this problem, apply the formula: $\small P=2(base+side)$ .

Since, the side length is equal to $\small \frac{base}{2}$ , the solution is:

$\small P=2(15+\frac{15}{2})$

$\small P=2(15+7.5)$

$\small P=2(22.5)=45$

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Example Question #2 : How To Find The Perimeter Of A Parallelogram

If a parallelogram has a base that is three times the length of the side, and the side length is equal to $\small \frac{3}{4}foot$ , what is the perimeter of the parallelogram in inches?

Possible Answers:

2ft

64in

72in

78in

Correct answer:

72in

Explanation:

The side length of this parallelogram is $\small \frac{3}{4}$ foot, which is equivalent to $\small 9$ inches because $12in=1ft \rightarrow \frac{3}{4}\cdot 12=\frac{36}{4}=9in$ .

Thus, the base must be $\small 9\times 3=27$ .

Then, apply the formula $\small p=2(base+side)$

$\small P=2(27+9)$

$\small P=2(36)=72$

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Example Question #351 : Plane Geometry

If a parallelogram has a base of $\small 9$ and a side length of $\small \frac{9}{3}$ , find the perimeter of the parallelogram.

Possible Answers:

$\small 21$

$\small 12$

$\small 24$

$\small 27$

Correct answer:

$\small 24$

Explanation:

To solve this problem, apply the formula: $\small p=2(base+side)$ .

Thus, the solution is:

$\small p=2\left(9+\frac{9}{3}\right)$

$\small p=2(9+3)$

$\small p=2(12)=24$

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Example Question #1 : How To Find An Angle In A Parallelogram

A parallelogram contains 2 angles measuring 135 and 45. What are the measures of the other 2 angles?

Possible Answers:

80,100

45,135

60,120

90,90

Any pair of numbers which add to 180

Correct answer:

45,135

Explanation:

Parallelograms have angles totalling 360 degrees, but also have matching pairs of angles at the ends of diagonals. Therefore the 2 additional angles must match the 2 given in the question.

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Example Question #1 : How To Find An Angle In A Parallelogram

Rhombus_with_missing_angles_

Using the above rhombus, find the measurement of angle

Possible Answers:

$70^\circ$

$180^\circ$

$110^\circ$

$50^\circ$

Correct answer:

$70^\circ$

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal 360 degrees. And, the adjacent interior angles must be supplementary angles (sum of 180 degrees)--i.e. angles A+D=180 degrees.

Thus, the solution is:

110+ $\measuredangle D=180$

$\measuredangle D=180-110=70$

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Example Question #3 : How To Find An Angle In A Parallelogram

Rhombus_with_missing_angles_

Using the above rhombus, find the measurement of angle .

Possible Answers:

$60^\circ$

$70^\circ$

$110^\circ$

$55^\circ$

Correct answer:

$110^\circ$

Explanation:

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Example Question #4 : How To Find An Angle In A Parallelogram

Custom_vt_rhomb_3

Using the above rhombus, find the sum of angle and angle .

Possible Answers:

$133^\circ$

$94^\circ$

$47^\circ$

$90^\circ$

Correct answer:

$94^\circ$

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal 360 degrees. And, the adjacent interior angles must be supplementary angles (sum of 180 degrees).

Thus, the solution is:

$\measuredangle H=47^\circ$

$\measuredangle F=47^\circ$

$47^\circ+47^\circ=94^\circ$

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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Example Question #2 : How To Find The Perimeter Of A Parallelogram

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Example Question #2 : How To Find The Perimeter Of A Parallelogram

Example Question #351 : Plane Geometry

Example Question #1 : How To Find An Angle In A Parallelogram

Example Question #1 : How To Find An Angle In A Parallelogram

Example Question #3 : How To Find An Angle In A Parallelogram

Example Question #4 : How To Find An Angle In A Parallelogram

All Intermediate Geometry Resources

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