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High School Math : Parallelograms

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

A parallelogram, with dimensions in cm, is shown below. Act1

What is the perimeter of the parallelogram, in cm?

Possible Answers:

$64+12\sqrt{3}$

Correct answer:

$64+12\sqrt{3}$

Explanation:

The triangle on the left side of the figure has a $30^{\circ}$ and a $90^{\circ}$ angle. Since all of the angles of a triangle must add up to $180^{\circ}$ , we can find the angle measure of the third angle:

30+90=120

$180-120=60^{\circ}$

Our third angle is $60^{\circ}$ and we have a 30-60-90 triangle.

A 30-60-90 triangle has sides that are in the corresponding ratio of $x-x\sqrt{3}-2x$ . In this case, the side opposite our $30^{\circ}$ angle is , so

x=6

We also now know that

$x\sqrt{3}=6\sqrt{3}$

2x=12

Now we know all of our missing side lengths. The right and left side of the parallelogram will each be . The bottom and top will each be $20+6\sqrt{3}$ . Let's combine them to find the perimeter:

Perimeter=2w+2l

$2\cdot (12)+2\cdot (20+6\sqrt{3})$

$24+40+12\sqrt{3}$

$64+12\sqrt{3}$

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Example Question #2 : Parallelograms

Find the perimeter of the following parallelogram:

Screen_shot_2014-02-27_at_6.43.30_pm

Possible Answers:

72m

40m

16m

30m

24m

Correct answer:

40m

Explanation:

The formula for the perimeter of a trapezoid is:

P=b_1+b_2+e_1+e_2 ,

where is the length of the base and is the length of the edge.

Opposite sides of a parallelogram have the same length. Therefore, both edges are and both bases are 12m .

Plugging in our values, we get:

P=12m+12m+8m+8m=40m

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Example Question #3 : Parallelograms

Find the perimeter of the following parallelogram:

Screen_shot_2014-03-01_at_9.26.41_pm

Possible Answers:

40m

75m

25m

50m

60m

Correct answer:

50m

Explanation:

The formula for the perimeter of a parallelogram is:

$P = 2(s_{long}) + 2(s_{short})$

where $s_{long}$ is the length of the longer side and $s_{short}$ is the length of the shorter side.

Plugging in our values, we get:

P = 2(16m) + 2(9m) = 50m

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Example Question #4 : Parallelograms

Find the perimeter of the following parallelogram:

Possible Answers:

$40 + 8\sqrt{2}\ m$

$36 + 8\sqrt{2}\ m$

$38 + 8\sqrt{2}\ m$

$34 + 8\sqrt{2}\ m$

$32 + 8\sqrt{2}\ m$

Correct answer:

$38 + 8\sqrt{2}\ m$

Explanation:

The formula for the perimeter of a parallelogram is

P = 2(side)+2(base) .

Plugging in our values, we get:

$P = 2(4\sqrt{2}\ m)+2(19\ m)$

$P = 38 + 8\sqrt{2}\ m$

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Example Question #1 : Parallelograms

ABCD is a parallelogram. BD = 5. The angles of triangle ABD are all equal. What is the perimeter of the parallelogram?

Figure_1

Possible Answers:

$10\sqrt{3}$

$15\sqrt{3}$

$11\sqrt{2}$

Correct answer:

Explanation:

If all of the angles in triangle ABD are equal and line BD divides the parallelogram, then all angles in triangle BDC must be equal as well.

We now have two equilateral triangles, so all sides of the triangles will be equal.

All sides therefore equal 5.

5+5+5+5 = 20

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Example Question #1 : Parallelograms

In the parallellogram, what is the value of ?

Screen_shot_2013-07-15_at_9.42.14_pm

Possible Answers:

$130^{\circ}$

$145^{\circ}$

$110^{\circ}$

$120^{\circ}$

$135^{\circ}$

Correct answer:

$130^{\circ}$

Explanation:

Opposite angles are equal, and adjacent angles must sum to 180.

Therefore, we can set up an equation to solve for z:

(z – 15) + 2z = 180

3z - 15 = 180

3z = 195

z = 65

Now solve for x:

2z = x = 130°

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Example Question #6 : Parallelograms

What is the area of a parallelogram with a base of and a height of ?

Possible Answers:

Correct answer:

Explanation:

To solve this question you must know the formula for the area of a parallelogram.

In this equation, is the length of the base and is the length of the height. We can plug in the side length for both base and height, as given in the question.

A=8*7

A=56

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Example Question #7 : Parallelograms

What is the area of a parallelogram with a base of and a height of ?

Possible Answers:

Correct answer:

Explanation:

To solve this question you must know the formula for the area of a parallelogram.

The formula is

So we can plug in the side length for both base and height to yield A=12*8

Perform the multiplication to arrive at the answer of A=96 .

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Example Question #8 : Parallelograms

Find the area of the following parallelogram:

Screen_shot_2014-02-27_at_6.43.30_pm

Possible Answers:

48m^2

96m^2

Cannot be determined from the given information.

$48\sqrt{3}m^2$

$96\sqrt{3}m^2$

Correct answer:

$48\sqrt{3}m^2$

Explanation:

The formula for the area of a parallelogram is:

A=(b)(h) ,

where is the length of the base and is the length of the height.

In order to the find the height of the parallelogram, use the formula for a 30-60-90 triangle:

$a-a\sqrt{3}-2a$ , where is the side opposite the $\measuredangle30$ .

The left side of the parallelogram forms the following 30-60-90 triangle:

$4m-4\sqrt{3}m-8m$ , where $4\sqrt{3}m$ is the length of the height.

Plugging in our values, we get:

$A=(12m)(4\sqrt{3}m)=48\sqrt{3}m^2$

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Example Question #9 : Parallelograms

Find the area of the following parallelogram:

Screen_shot_2014-03-01_at_9.26.41_pm

Possible Answers:

$144\sqrt{7}m^2$

$54\sqrt{7}m^2$

$36\sqrt{7}m^2$

$45\sqrt{7}m^2$

$72\sqrt{7}m^2$

Correct answer:

$45\sqrt{7}m^2$

Explanation:

Use the Pythagorean Theorem to determine the length of the diagonal:

A^2 + B^2 = C^2

(9m)^2 + B^2 = (16m^2)

B^2 = 175m^2

$B = 5 \sqrt{7}m$

The area of the parallelogram is twice the area of the right triangles:

$A_{Triangle} = \frac{1}{2} (b)(h)$

$A_{Triangle} = \frac{1}{2} (9m)(5m\sqrt{7}) = \frac{45m^2\sqrt{7}}{2}$

$A_{Parallelogram} = 2 (A_{Triangle}) = 2\left(\frac{45m^2\sqrt{7}}{2}\right)=45m^2\sqrt{7}$

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High School Math : Parallelograms

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

Example Question #2 : Parallelograms

Example Question #3 : Parallelograms

Example Question #4 : Parallelograms

Example Question #1 : Parallelograms

Example Question #1 : Parallelograms

Example Question #6 : Parallelograms

Example Question #7 : Parallelograms

Example Question #8 : Parallelograms

Example Question #9 : Parallelograms

All High School Math Resources

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