Trapezoids - Math
Card 1 of 72
Find the measure of angle 
in the isosceles trapezoid pictured below.
Find the measure of angle
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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**°**.
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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What is the area of this regular trapezoid?
What is the area of this regular trapezoid?
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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?
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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?
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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:
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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:
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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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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 another base, and is the length of the height.
Use the Pythagorean Theorem to find the height of the trapezoid:
Plugging in our values, we get:
The formula for the area of a trapezoid is:
where
Use the Pythagorean Theorem to find the height of the trapezoid:
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
The formula for the area of a trapezoid is
.
Use the Pythagorean Theorem to find the length of the height:
Plugging in our values, we get:
The formula for the area of a trapezoid is
Use the Pythagorean Theorem to find the length of the height:
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
The formula for the area of a trapezoid is
,
where 
is the base of the trapezoid and 
is the height of the trapezoid.
Use the formula for a 
triangle to find the length of the base and height:
Use the formula for a 
triangle to find the length of the base and height:
Plugging in our values, we get:
The formula for the area of a trapezoid is
where
Use the formula for a
Use the formula for a
Plugging in our values, we get:
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The following quadrilaterals are similar. Solve for 
.
(Figure not drawn to scale).
The following quadrilaterals are similar. Solve for
(Figure not drawn to scale).
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When polygons are similar, the sides will have the same ratio to one another. Set up the appropriate proportions.
Cross multiply.
When polygons are similar, the sides will have the same ratio to one another. Set up the appropriate proportions.
Cross multiply.
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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 perimeter of the isoceles trapezoid (in.)?
This figure is an isosceles trapezoid with bases of 6 in and 18 in and a side of 10 in.
What is the perimeter of the isoceles trapezoid (in.)?
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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.
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.
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Find the perimeter of the following trapezoid:
Find the perimeter of the following trapezoid:
Tap to reveal answer
The formula for the perimeter of a trapezoid is:
Where 
is the base and 
is the edge
Plugging in our values, we get:
The formula for the perimeter of a trapezoid is:
Where
Plugging in our values, we get:
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Find the perimeter of the following trapezoid:
Find the perimeter of the following trapezoid:
Tap to reveal answer
Use the formula for triangles in order to find the lengths of all the sides and bases.
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 perimeter of a trapezoid is:
Where is the base and is the edge
Plugging in our values, we get:
Use the formula for
The formula is:
Where
Beginning with the
Creating another
The formula for the perimeter of a trapezoid is:
Where
Plugging in our values, we get:
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Determine the perimeter of the following trapezoid:
Determine the perimeter of the following trapezoid:
Tap to reveal answer
The formula for the perimeter of a trapezoid is:
,
where 
is the length of the base and 
is the length of the edge.
Plugging in our values, we get:
The formula for the perimeter of a trapezoid is:
where
Plugging in our values, we get:
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Find the perimeter of the following trapezoid:
Find the perimeter of the following trapezoid:
Tap to reveal answer
The formula for the perimeter of a trapezoid is:
,
where is the length of the base and is the length of the edge.
Plugging in our values, we get:
The formula for the perimeter of a trapezoid is:
where
Plugging in our values, we get:
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Find the perimeter of the following trapezoid:
Find the perimeter of the following trapezoid:
Tap to reveal answer
The formula for the perimeter of a trapezoid is
.
Use the formula for a 
triangle to find the length of the base and side:
Use the formula for a 
triangle to find the length of the base and side:
Plugging in our values, we get:
The formula for the perimeter of a trapezoid is
Use the formula for a
Use the formula for a
Plugging in our values, we get:
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Find the measure of angle in the isosceles trapezoid pictured below.
Find the measure of angle
Tap to reveal answer
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**°**.
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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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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