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Advanced Geometry : How to find the area of a trapezoid

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Example Questions

Example Question #1 : Trapezoids

Which of the following shapes is a trapezoid?

Shapes

Possible Answers:

C, D

B, C, D

None

B, D

Correct answer:

B, D

Explanation:

A trapezoid is a four-sided shape with straight sides that has a pair of opposite parallel sides. The other sides may or may not be parallel. A square and a rectangle are both considered trapezoids.

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Example Question #2 : Trapezoids

What is the area of the following trapezoid?

Trapezoid

Possible Answers:

32m^2

24m^2

80m^2

36m^2

40m^2

Correct answer:

36m^2

Explanation:

The formula for the area of a trapezoid is:

$A = \frac{1}{2} (b_{1} + b_{2})(h)$ ,

where $b_{1}$ is the value of the top base, $b_{2}$ is value of the bottom base, and is the value of the height.

Plugging in our values, we get:

$A = \frac{1}{2} (8\: m + 10\: m)(4\: m)$

$A = \frac{1}{2} (18\: m)(4\: m)$

$A = (9\: m)(4\: m) = 36\: m^2$

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Example Question #3 : Trapezoids

Screen_shot_2015-03-06_at_2.30.09_pm

What is the area of the trapezoid pictured above in square units?

Possible Answers:

168

238

119

Correct answer:

119

Explanation:

The formula for the area of a trapezoid is the average of the bases times the height,

$A=\frac{b_{1}+b_{2}}{2}h$ .

Looking at this problem and when the appropriate values are plugged in, the formula yields:

$A=(\frac{10+24}{2})7$

$A=\frac{34}{2}\cdot 7$

$A=\frac{238}{2}=119$

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Example Question #4 : Trapezoids

Screen_shot_2015-03-06_at_2.44.49_pm

What is the height of the trapezoid pictured above?

Possible Answers:

Correct answer:

Explanation:

To find the height, we must introduce two variables, $b_{1}, b_{2}$ , each representing the bases of the triangles on the outside, so that $b_{1}+b_{2}+11=25, b_{1}+b_{2}=14$ . (Equation 1)

The next step is to set up two Pythagorean Theorems,

$13^2=b_{1}^2+h^2, 15^2=b_{2}^2+h^2$ (Equation 2, 3)

The next step is a substitution from the first equation,

$b_{1}=14-b_{2}, b_{1}^2=196-28b_{2}+b_{2}^2$ (Equation 4)

and plugging it in to the second equation, yielding

$13^2=196-28b_{2}+b_{2}^2+h^2$ (Equation 5)

The next step is to substitute from Equation 3 into equation 5,

$h^2=15^2-b_{2}^2$ , $169=196-28b_{2}+b_{2}^2+225-b_{2}^2$ which simplifies to

$-252=-28b_{2}, b_{2}=9$

Once we have one of the bases, just plug into the Pythagorean Theorem, 225=81+h^2, 144=h^2, h=12

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Example Question #5 : Trapezoids

A isosceles trapezoid with sides , , , and has a height of , what is the area?

Possible Answers:

194

138

180

160

Correct answer:

180

Explanation:

An isosceles trapezoid has two sides that are the same length and those are not the bases, so the bases are 10 and 20.

The area of the trapezoid then is:

$A=\frac{b_{1}+b_{2}}{2}h=\frac{10+20}{2}12=15 \cdot 12=180$

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Example Question #1 : Trapezoids

If the height of a trapezoid is , bottom base is , and the top base is , what is the area?

Possible Answers:

300

200

150

Correct answer:

150

Explanation:

The formula for finding the area of a trapezoid is:

$A=\frac{1}{2}(b1+b2)h$

Substitute the given values to find the area.

$A=\frac{1}{2}(20+10)(10)$

$A= \frac{1}{2}(30)(10)$

$A=\frac{1}{2}(300)$

A=150

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Example Question #2 : Trapezoids

Find the area of a trapezoid with bases of length $12\:cm$ and $15\:cm$ and a height of $7\:cm$ .

Possible Answers:

$105\:cm^2$

$189\:cm^2$

$84\:cm^2$

$52.5\:cm^2$

$94.5\:cm^2$

Correct answer:

$94.5\:cm^2$

Explanation:

The formula for the area of a trapezoid is:

$A = \frac{a + b}{2}h$

Where and are the bases and is the height. Using this formula and the given values, we get:

$A = \frac{12\:cm + 15\:cm}{2}\left ( 7\:cm) = 94.5\:cm^2$

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Example Question #2 : Trapezoids

Find the area of a trapezoid with bases of $8\:cm$ and $11\:cm$ and a height of $14\:cm$ .

Possible Answers:

$133\:cm^2$

$112\:cm^2$

$88\:cm^2$

$66.5\:cm^2$

$121\:cm^2$

Correct answer:

$133\:cm^2$

Explanation:

The formula for the area of a trapezoid is:

$A = \frac{a + b}{2}h$

Where and are the bases and is the height. Using this formula and the given values, we get:

$A = \frac{8\:cm + 12\:cm}{2}\left ( 14\:cm ) = 133\:cm^2$

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Example Question #3 : Trapezoids

Trapezoid_1

Find the area of the above trapezoid.

Possible Answers:

$435\:units^2$

$208\:units^2$

$714\:units^2$

$195\:units^2$

$315\:units^2$

Correct answer:

$315\:units^2$

Explanation:

The formula for the area of a trapezoid is:

$A = \frac{a + b}{2}h$

Where and are the bases and is the height. Using this formula and the given values, we get:

$A = \frac{13\:units + 29\:units}{2}\left ( 15\:units ) = 315\:units^2$

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Example Question #4 : Trapezoids

Trapezoid_2

Find the area of the above trapezoid.

Possible Answers:

$50\:units^2$

$20\:units^2$

$40\:units^2$

$28\:units^2$

$35\:units^2$

Correct answer:

$28\:units^2$

Explanation:

The formula for the area of a trapezoid is:

$A = \frac{a + b}{2}h$

Where and are the bases and is the height. Using this formula and the given values, we get:

$A = \frac{4\:units + 10\:units}{2}\left ( 4\:units\right ) = 28\:units^2$

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Advanced Geometry : How to find the area of a trapezoid

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #1 : Trapezoids

Example Question #2 : Trapezoids

Example Question #3 : Trapezoids

Example Question #4 : Trapezoids

Example Question #5 : Trapezoids

Example Question #1 : Trapezoids

Example Question #2 : Trapezoids

Example Question #2 : Trapezoids

Example Question #3 : Trapezoids

Example Question #4 : Trapezoids

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