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High School Math : Plane Geometry

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Example Questions

Example Question #171 : Plane Geometry

Find the perimeter of the following trapezoid:

Trapezoid

Possible Answers:

68m

72m

70m

62m

64m

Correct answer:

68m

Explanation:

The formula for the perimeter of a trapezoid is:

$P= b_{1} +b_{2}+e_{1}+e_{2}$

Where is the base and is the edge

Plugging in our values, we get:

P= 16m +26m+13m+13m=68m

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

Find the perimeter of the following trapezoid:

Trapezoid_angles

Possible Answers:

$44+6\sqrt{3}m$

$56+12\sqrt{3}m$

$44+12\sqrt{3}m$

56m

44m

Correct answer:

$44+12\sqrt{3}m$

Explanation:

Use the formula for 30-60-90 triangles in order to find the lengths of all the sides and bases.

The formula is:

$a-a\sqrt{3}-2a$

Where is the length of the side opposite the $\measuredangle 30$ .

Beginning with the 12m side, if we were to create a 30-60-90 triangle, the length of the base is $6\sqrt{3}m$ , and the height is .

Creating another 30-60-90 triangle on the left, we find the height is , the length of the base is $2\sqrt{3}m$ , and the side is $4\sqrt{3}m$ .

The formula for the perimeter of a trapezoid is:

$P= b_{1} +b_{2}+e_{1}+e_{2}$

Where is the base and is the edge

Plugging in our values, we get:

$P= (16m) +(16m+6\sqrt{3}m+2\sqrt{3}m)+(12m)+(4\sqrt{3}m)$

$P=44+12\sqrt{3}m$

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Example Question #3 : How To Find The Perimeter Of A Trapezoid

Determine the perimeter of the following trapezoid:

Screen_shot_2014-02-27_at_6.39.24_pm

Possible Answers:

28m

20m

21m

25m

24m

Correct answer:

21m

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.

Plugging in our values, we get:

P=7m+5m+4m+5m=21m

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Example Question #4 : How To Find The Perimeter Of A Trapezoid

Find the perimeter of the following trapezoid:

Screen_shot_2014-02-27_at_6.47.22_pm

Possible Answers:

90m

70m

80m

88m

78m

Correct answer:

88m

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.

Plugging in our values, we get:

P=20m+18m+20m+30m=88m

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Example Question #21 : Quadrilaterals

Find the perimeter of the following trapezoid:

Possible Answers:

$35+5\sqrt{2}+5\sqrt{3}\ m$

$15+5\sqrt{2}+10\sqrt{3}\ m$

$35+10\sqrt{2}+5\sqrt{3}\ m$

$15+5\sqrt{2}+5\sqrt{3}\ m$

$35+5\sqrt{2}+10\sqrt{3}\ m$

Correct answer:

$35+5\sqrt{2}+5\sqrt{3}\ m$

Explanation:

The formula for the perimeter of a trapezoid is

P = base_1+base_2+side_1+side_2 .

Use the formula for a 30-60-90 triangle to find the length of the base and side:

$a-2a-a\sqrt{3}$

$5\ m-10\ m-5\sqrt{3}\ m$

Use the formula for a 45-45-90 triangle to find the length of the base and side:

a-a-2a

$5\ m-5\ m-5\sqrt{2}\ m$

Plugging in our values, we get:

$P = 5\sqrt{2}\ m+10\ m+10\ m+5\sqrt{3}\ m+10\ m+5\ m$

$P = 35+5\sqrt{2}+5\sqrt{3}\ m$

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Example Question #12 : Parallelograms

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:

16m

30m

24m

72m

40m

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 #2 : Parallelograms

Find the perimeter of the following parallelogram:

Screen_shot_2014-03-01_at_9.26.41_pm

Possible Answers:

25m

75m

60m

40m

50m

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 #3 : Parallelograms

Find the perimeter of the following parallelogram:

Possible Answers:

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

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

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

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

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

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 #2 : Quadrilaterals

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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High School Math : Plane Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #171 : Plane Geometry

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

Example Question #3 : How To Find The Perimeter Of A Trapezoid

Example Question #4 : How To Find The Perimeter Of A Trapezoid

Example Question #21 : Quadrilaterals

Example Question #12 : Parallelograms

Example Question #2 : Parallelograms

Example Question #2 : Parallelograms

Example Question #3 : Parallelograms

Example Question #2 : Quadrilaterals

All High School Math Resources

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