Trapezoids - Math
Card 1 of 646
Note: Figure NOT drawn to scale
The above figure shows Square 
.
Which is the greater quantity?
(a) The area of Trapezoid 
(b) The area of Trapezoid 
Note: Figure NOT drawn to scale
The above figure shows Square
Which is the greater quantity?
(a) The area of Trapezoid
(b) The area of Trapezoid
Tap to reveal answer
The easiest way to answer the question is to locate 
on 
such that 
:
Trapezoids 
and 
have the same height, which is 
. Their bases, by construction, have the same lengths - 
and 
. Therefore, Trapezoids 
and 
have the same area.
Since , it follows that 
, and 
. It follows that Trapezoid 
is greater in area than Trapezoids 
and 
, and Trapezoid is less in area.
The easiest way to answer the question is to locate
Trapezoids
Since
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In the trapezoid below, find the degree measure of 
.
In the trapezoid below, find the degree measure of
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In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 
degrees.
and the angle measuring 
degrees are adjacent angles that are supplementary.
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to
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In the trapezoid below, find the angle measurement of 
.
In the trapezoid below, find the angle measurement of
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In a trapezoid, all the interior angles add up to 
degrees.
is 
degrees.
In a trapezoid, all the interior angles add up to
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In the trapezoid below, find the angle measurement of 
.
In the trapezoid below, find the angle measurement of
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All the interior angles in a trapezoid add up to 
.
is 
degrees.
All the interior angles in a trapezoid add up to
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In the trapezoid below, find the angle measurement of 
.
In the trapezoid below, find the angle measurement of
Tap to reveal answer
All the interior angles in a trapezoid add up to 
.
is 
degrees.
All the interior angles in a trapezoid add up to
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In the trapezoid below, find the degree measurement of 
.
In the trapezoid below, find the degree measurement of
Tap to reveal answer
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 
degrees.
and the angle measuring 
degrees are adjacent angles that are supplementary.
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to
← Didn't Know|Knew It →
In the trapezoid below, find the degree measurement of 
.
In the trapezoid below, find the degree measurement of
Tap to reveal answer
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 
degrees.
and the angle measuring 
degrees are adjacent angles that are supplementary.
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to
← Didn't Know|Knew It →
In the trapezoid below, find the degree measurement of 
.
In the trapezoid below, find the degree measurement of
Tap to reveal answer
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 
degrees.
and the angle measuring 
degrees are adjacent angles that are supplementary.
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to
← Didn't Know|Knew It →
In the trapezoid below, find the degree measurement of 
.
In the trapezoid below, find the degree measurement of
Tap to reveal answer
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 
degrees.
and the angle measuring 
degrees are adjacent angles that are supplementary.
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to
← Didn't Know|Knew It →
In the trapezoid below, find the degree measurement of 
.
In the trapezoid below, find the degree measurement of
Tap to reveal answer
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 
degrees.
and the angle measuring 
degrees are adjacent angles that are supplementary.
Therefore, we can write the following equation and solve for a.
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to
Therefore, we can write the following equation and solve for a.
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In the trapezoid below, find the degree measurement of 
.
In the trapezoid below, find the degree measurement of
Tap to reveal answer
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 
degrees.
and the angle measuring 
degrees are adjacent angles that are supplementary.
Therefore, we can write the following equation and solve for z.
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to
Therefore, we can write the following equation and solve for z.
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In the trapezoid below, find the degree measurement of 
.
In the trapezoid below, find the degree measurement of
Tap to reveal answer
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 
degrees.
and the angle measuring 
degrees are adjacent angles that are supplementary.
Therefore, we can write the following equations and solve for y.
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to
Therefore, we can write the following equations and solve for y.
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In the trapezoid below, find the degree measurement of 
.
In the trapezoid below, find the degree measurement of
Tap to reveal answer
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 
degrees.
and the angle measuring 
degrees are adjacent angles that are supplementary.
Thus, we can write the following equation and solve for x.
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to
Thus, we can write the following equation and solve for x.
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What is the area of this regular trapezoid?
What is the area of this regular trapezoid?
Tap to reveal answer
To solve this question, you must divide the trapezoid into a rectangle and two right triangles. Using the Pythagorean Theorem, you would calculate the height of the triangle which is 4. The dimensions of the rectangle are 5 and 4, hence the area will be 20. The base of the triangle is 3 and the height of the triangle is 4. The area of one triangle is 6. Hence the total area will be 20+6+6=32. If you forget to split the shape into a rectangle and TWO triangles, or if you add the dimensions of the trapezoid, you could arrive at 26 as your answer.
To solve this question, you must divide the trapezoid into a rectangle and two right triangles. Using the Pythagorean Theorem, you would calculate the height of the triangle which is 4. The dimensions of the rectangle are 5 and 4, hence the area will be 20. The base of the triangle is 3 and the height of the triangle is 4. The area of one triangle is 6. Hence the total area will be 20+6+6=32. If you forget to split the shape into a rectangle and TWO triangles, or if you add the dimensions of the trapezoid, you could arrive at 26 as your answer.
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What is the area of the trapezoid above if a = 2, b = 6, and h = 4?
What is the area of the trapezoid above if a = 2, b = 6, and h = 4?
Tap to reveal answer
Area of a Trapezoid = ½(a+b)*h
= ½ (2+6) * 4
= ½ (8) * 4
= 4 * 4 = 16
Area of a Trapezoid = ½(a+b)*h
= ½ (2+6) * 4
= ½ (8) * 4
= 4 * 4 = 16
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A trapezoid has a base of length 4, another base of length s, and a height of length s. A square has sides of length s. What is the value of s such that the area of the trapezoid and the area of the square are equal?
A trapezoid has a base of length 4, another base of length s, and a height of length s. A square has sides of length s. What is the value of s such that the area of the trapezoid and the area of the square are equal?
Tap to reveal answer
In general, the formula for the area of a trapezoid is (1/2)(a + b)(h), where a and b are the lengths of the bases, and h is the length of the height. Thus, we can write the area for the trapezoid given in the problem as follows:
area of trapezoid = (1/2)(4 + s)(s)
Similarly, the area of a square with sides of length a is given by _a_2. Thus, the area of the square given in the problem is _s_2.
We now can set the area of the trapezoid equal to the area of the square and solve for s.
(1/2)(4 + s)(s) = _s_2
Multiply both sides by 2 to eliminate the 1/2.
(4 + s)(s) = 2_s_2
Distribute the s on the left.
4_s_ + _s_2 = 2_s_2
Subtract _s_2 from both sides.
4_s_ = _s_2
Because s must be a positive number, we can divide both sides by s.
4 = s
This means the value of s must be 4.
The answer is 4.
In general, the formula for the area of a trapezoid is (1/2)(a + b)(h), where a and b are the lengths of the bases, and h is the length of the height. Thus, we can write the area for the trapezoid given in the problem as follows:
area of trapezoid = (1/2)(4 + s)(s)
Similarly, the area of a square with sides of length a is given by _a_2. Thus, the area of the square given in the problem is _s_2.
We now can set the area of the trapezoid equal to the area of the square and solve for s.
(1/2)(4 + s)(s) = _s_2
Multiply both sides by 2 to eliminate the 1/2.
(4 + s)(s) = 2_s_2
Distribute the s on the left.
4_s_ + _s_2 = 2_s_2
Subtract _s_2 from both sides.
4_s_ = _s_2
Because s must be a positive number, we can divide both sides by s.
4 = s
This means the value of s must be 4.
The answer is 4.
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This figure is an isosceles trapezoid with bases of 6 in and 18 in and a side of 10 in.
What is the area of the isoceles trapezoid?
This figure is an isosceles trapezoid with bases of 6 in and 18 in and a side of 10 in.
What is the area of the isoceles trapezoid?
Tap to reveal answer
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:
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 
.
Multiply the average of the bases (12) by the height (8) to get an area of 96.
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:
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
Multiply the average of the bases (12) by the height (8) to get an area of 96.
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Find the area of the following trapezoid:
Find the area of the following trapezoid:
Tap to reveal answer
The formula for the area of a trapezoid is:
Where 
is the length of one base, 
is the length of the other base, and 
is the height.
To find the height of the trapezoid, use a Pythagorean triple:
Plugging in our values, we get:
The formula for the area of a trapezoid is:
Where
To find the height of the trapezoid, use a Pythagorean triple:
Plugging in our values, we get:
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Find the area of the following trapezoid:
Find the area of the following trapezoid:
Tap to reveal answer
Use the formula for 
triangles in order to find the length of the bottom base and the height.
The formula is:
Where 
is the length of the side opposite the 
.
Beginning with the 
side, if we were to create a 
triangle, the length of the base is 
, and the height is 
.
Creating another triangle on the left, we find the height is , the length of the base is 
, and the side is 
.
The formula for the area of a trapezoid is:
Where is the length of one base, is the length of the other base, and is the height.
Plugging in our values, we get:
Use the formula for
The formula is:
Where
Beginning with the
Creating another
The formula for the area of a trapezoid is:
Where
Plugging in our values, we get:
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Determine the area of the following trapezoid:
Determine the area of the following trapezoid:
Tap to reveal answer
The formula for the area of a trapezoid is:
,
where 
is the length of one base, 
is the length of another base, and 
is the length of the height.
Plugging in our values, we get:
The formula for the area of a trapezoid is:
where
Plugging in our values, we get:
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