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High School Math : Trapezoids

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Example Questions

Example Question #1 : How To Find The Area Of A Trapezoid

This figure is an isosceles trapezoid with bases of 6 in and 18 in and a side of 10 in. Isoceles_trapezoid

What is the area of the isoceles trapezoid?

Possible Answers:

120

180

Correct answer:

Explanation:

In order to find the area of an isoceles trapezoid, you must average the bases and multiply by the height.

The average of the bases is straight forward:

$\frac{6+18}{2}=12$

In order to find the height, you must draw an altitude. This creates a right triangle in which one of the legs is also the height of the trapezoid. You may recognize the Pythagorean triple (6-8-10) and easily identify the height as 8. Otherwise, use $a^{2}+b^{2}=c^{2}$ .

$36+b^{2}=100$

$b^{2}=64$

b=8

Multiply the average of the bases (12) by the height (8) to get an area of 96.

Isoceles_trapezoid_explained

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

Find the measure of angle in the isosceles trapezoid pictured below.

Screen_shot_2013-03-18_at_3.32.40_pm

Possible Answers:

$108^{\circ}$

$18^{\circ}$

$118^{\circ}$

$72^{\circ}$

$36^{\circ}$

Correct answer:

$108^{\circ}$

Explanation:

The sum of the angles in any quadrilateral is 360°, and the properties of an isosceles trapezoid dictate that the sets of angles adjoined by parallel lines (in this case, the bottom set and top set of angles) are equal. Subtracting 2(72°) from 360° gives the sum of the two top angles, and dividing the resulting 216° by 2 yields the measurement of x, which is 108°.

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

This figure is an isosceles trapezoid with bases of 6 in and 18 in and a side of 10 in. Isoceles_trapezoid

What is the perimeter of the isoceles trapezoid (in.)?

Possible Answers:

Correct answer:

Explanation:

The perimeter of the isoceles trapezoid is the sum of all the sides. You can assume the left side is also 10 in. because it is an isoceles trapezoid.

6+18+10+10=44

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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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High School Math : Trapezoids

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find The Area Of A Trapezoid

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

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

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

All High School Math Resources

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