How to find the length of the side of a trapezoid - Math
Card 1 of 136
In the above diagram, which depicts Trapezoid 
, 
and 
. Which is the greater quantity?
(a) 
(b) 24
In the above diagram, which depicts Trapezoid
(a)
(b) 24
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To see that (b) is the greater quantity of the two, it suffices to construct the midsegment of the trapezoid - the segment which has as its endpoints the midpoints of legs 
and 
. Since 
and 
, the midsegment, 
, is positioned as follows:
The length of the midsegment is half the sum of the bases, so
, so 
.
To see that (b) is the greater quantity of the two, it suffices to construct the midsegment of the trapezoid - the segment which has as its endpoints the midpoints of legs
The length of the midsegment is half the sum of the bases, so
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Figure NOT drawn to scale.
The above figure depicts Trapezoid 
with midsegment 
. 
, and 
.
Give the area of Trapezoid 
in terms of 
.
Figure NOT drawn to scale.
The above figure depicts Trapezoid
Give the area of Trapezoid
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The midsegment of a trapezoid has as its length half the sum of the lengths of the bases, which here are 
and 
:
Therefore, 
The area of Trapezoid 
is one half multiplied by the height, 
, multiplied by the sum of the lengths of the bases, 
and 
. The midsegment of a trapezoid bisects both legs, so 
, and the area is
The midsegment of a trapezoid has as its length half the sum of the lengths of the bases, which here are
Therefore,
The area of Trapezoid
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The above figure depicts Trapezoid 
with midsegment 
. Express 
in terms of 
.
The above figure depicts Trapezoid
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The midsegment of a trapezoid has as its length half the sum of the lengths of the bases, which here are and :
The correct choice is 
.
The midsegment of a trapezoid has as its length half the sum of the lengths of the bases, which here are
The correct choice is
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Suppose the area of the trapezoid is 
, with a height of 
and a base of 
. What must be the length of the other base?
Suppose the area of the trapezoid is
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Write the formula for finding the area of a trapezoid.
Substitute the givens and solve for either base.
Write the formula for finding the area of a trapezoid.
Substitute the givens and solve for either base.
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If the area of a trapezoid is 
, the height of the trapezoid is 
, and the base length is 
, what must be the length of the other base?
If the area of a trapezoid is
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Write the formula for the area of a trapezoid.
Substitute all the given values and solve for the base.
Write the formula for the area of a trapezoid.
Substitute all the given values and solve for the base.
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An isosceles trapezoid has base measurements of 
and 
. The perimeter of the trapezoid is 
. Find the length for one of the two remaining sides.
An isosceles trapezoid has base measurements of
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To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one 
Base two 
(leg), where the length of "leg" is one of the two equivalent nonparallel sides.
Thus, the solution is:
Check the solution by plugging in the answer:
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one
Thus, the solution is:
Check the solution by plugging in the answer:
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An isosceles trapezoid has base measurements of 
and 
. Additionally, the isosceles trapezoid has a height of 
. Find the length for one of the two missing sides.
An isosceles trapezoid has base measurements of
Tap to reveal answer
In order to solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.
This problem provides the lengths for each of the bases as well as the height of the isosceles trapezoid. In order to find the length for one of the two equivalent nonparallel legs of the trapezoid, first use the height of the trapezoid to form right triangles on the interior of the trapezoid that each have a base length of 
. See image below:
Note: the base length of 
can be found by subtracting the lengths of the two bases, then dividing that difference in half:
Now, apply the formula 
, where 
the length for one of the two equivalent nonparallel legs of the trapezoid.
Thus, the solution is:
In order to solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.
This problem provides the lengths for each of the bases as well as the height of the isosceles trapezoid. In order to find the length for one of the two equivalent nonparallel legs of the trapezoid, first use the height of the trapezoid to form right triangles on the interior of the trapezoid that each have a base length of
Note: the base length of
Now, apply the formula
Thus, the solution is:
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The isosceles trapezoid shown above has base measurements of 
and 
. Additionally, the trapezoid has a height of 
. Find the length of side 
.
The isosceles trapezoid shown above has base measurements of
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In this problem the lengths for each of the bases and the height of the isosceles trapezoid is provided in the question prompt. In order to find the length for one of the two equivalent nonparallel legs of the trapezoid (side 
), first use the height of the trapezoid to form right triangles on the interior of the trapezoid that each have a base length of 
.
The base of the interior triangles is equal to 
because the difference between the two bases is equal to 
. And, this difference must be divided evenly in half because the isosceles trapezoid is symmetric--due to the two equivalent nonparallel sides and the two nonequivalent parallel bases.
Now, apply the pythagorean theorem: 
, where 
.
Thus, 
In this problem the lengths for each of the bases and the height of the isosceles trapezoid is provided in the question prompt. In order to find the length for one of the two equivalent nonparallel legs of the trapezoid (side
The base of the interior triangles is equal to
Now, apply the pythagorean theorem:
Thus,
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Using the trapezoid shown above, find the length of side 
.
Using the trapezoid shown above, find the length of side
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In order to find the length of side 
, first note that the vertical side that has a length of 
and the base side with length 
must be perpendicular because they form a right angle. This means that the height of the trapezoid must equal 
. A right triangle can be formed on the interior of the trapezoid that has a height of 
and a base lenght of 
The base length can be derived by finding the difference between the two nonequivalent parallel bases.
Thus, the solution can be found by applying the formula: 
, where 
In order to find the length of side
Thus, the solution can be found by applying the formula:
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Using the isosceles trapezoid shown above, find the length for one of the two nonparallel equivalent sides.
Using the isosceles trapezoid shown above, find the length for one of the two nonparallel equivalent sides.
Tap to reveal answer
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one Base two (leg), where the length of "leg" is one of the two equivalent nonparallel sides.
Thus, the solution is:
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one
Thus, the solution is:
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An isosceles trapezoid has base measurements of 
and 
. The perimeter of the trapezoid is 
. Find the length for one of the two remaining sides.
An isosceles trapezoid has base measurements of
Tap to reveal answer
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one Base two (leg), where the length of "leg" is one of the two equivalent nonparallel sides.
Note: once you find the answer in inches, convert that quantity to an equivalent amount in feet.
Thus, the solution is:
inch is equal to 
foot. Therefore, 
inches is equvalent to 
foot.
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one
Note: once you find the answer in inches, convert that quantity to an equivalent amount in feet.
Thus, the solution is:
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An isosceles trapezoid has base measurements of 
and 
, respectively. Additionally, the isosceles trapezoid has a height that is 
the measurement of the larger base. Find the length for one of the two equivalent nonparallel sides.
An isosceles trapezoid has base measurements of
Tap to reveal answer
In order to solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.
This problem provides the lengths for each of the bases as well as informataion regarding the height of the isosceles trapezoid. In order to find the length for one of the two equivalent nonparallel legs of the trapezoid, use the height of the trapezoid to form right triangles on the interior of the trapezoid that each have a base length of 
. The interior triangle base length of 
can be found by subtracting the lengths of the two bases, then dividing that difference in half:
In order to calculate the exact height of the isosceles trapezoid (as well as the interior triangle), find 
of the larger base. Since the largest base of the trapezoid is 
, the height of the trapezoid is: 
Now you have enough information to apply the formula 
, where 
one of the missing sides.
The final solution is:
In order to solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.
This problem provides the lengths for each of the bases as well as informataion regarding the height of the isosceles trapezoid. In order to find the length for one of the two equivalent nonparallel legs of the trapezoid, use the height of the trapezoid to form right triangles on the interior of the trapezoid that each have a base length of
In order to calculate the exact height of the isosceles trapezoid (as well as the interior triangle), find
Now you have enough information to apply the formula
The final solution is:
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An isosceles trapezoid has one base measurement of 
and the length for one of the nonparallel sides is 
. The perimeter of the trapezoid is 
. Find the length for the other base of the trapezoid.
An isosceles trapezoid has one base measurement of
Tap to reveal answer
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.
Therefore, use the given information to apply the formula:
Perimeter= Base one Base two (leg), where the length of "leg" is one of the two equivalent nonparallel sides.
Thus, the solution is:
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.
Therefore, use the given information to apply the formula:
Perimeter= Base one
Thus, the solution is:
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An isosceles trapezoid has base measurements of 
and 
. The perimeter of the trapezoid is 
. Find the length for one of the two remaining sides.
An isosceles trapezoid has base measurements of
Tap to reveal answer
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one Base two (leg), where the length of "leg" is one of the two equivalent nonparallel sides.
Thus, the solution is:
Check the solution by plugging in the answer:
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides can be found using the following formula: Perimeter= Base one
Thus, the solution is:
Check the solution by plugging in the answer:
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An isosceles trapezoid has one base measurement of 
and the length for one of the nonparallel sides is 
. The perimeter of the trapezoid is 
. Find the length for the other base of the trapezoid.
An isosceles trapezoid has one base measurement of
Tap to reveal answer
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.
Therefore, use the given information to apply the formula:
Perimeter= Base one Base two (leg), where the length of "leg" is one of the two equivalent nonparallel sides.
Thus, the solution is:
To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.
Therefore, use the given information to apply the formula:
Perimeter= Base one
Thus, the solution is:
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Using the isosceles trapezoid shown above, find a possible base measurement for a similar trapezoid where the largest base measurement is 
.
Using the isosceles trapezoid shown above, find a possible base measurement for a similar trapezoid where the largest base measurement is
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In order for two trapezoids to be similar their corresponding sides must have the same ratio. Since the largest base length in the image is 
and the corresponding side is 
, the other base must also be 
times greater than the corresponding side shown in the image.
The smaller base shown in the image has a length of 
, thus the corresponding side in the similar trapezoid must equal: 
.
In order for two trapezoids to be similar their corresponding sides must have the same ratio. Since the largest base length in the image is
The smaller base shown in the image has a length of
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Using the image shown above, find the lenght for one of the two nonparallel equivalent sides for a similar trapezoid where the perimeter is equal to 
.
Using the image shown above, find the lenght for one of the two nonparallel equivalent sides for a similar trapezoid where the perimeter is equal to
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In order for two trapezoids to be similar their corresponding sides must have the same ratio. Since the perimeter in the image is 
and the corresponding perimeter is 
, the corresponding sides must also be 
times greater than the corresponding sides shown in the image.
The nonparallel equivalent sides shown in the image have a length of , thus the corresponding side in the similar trapezoid must equal: 
.
In order for two trapezoids to be similar their corresponding sides must have the same ratio. Since the perimeter in the image is
The nonparallel equivalent sides shown in the image have a length of
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Quadrilateral 
such that 
, 
and 
. Which of the following correctly describes this quadrilateral?
Quadrilateral
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Quadrilateral 
has at least one pair of parallel sides, 
and 
. The figure is, by definition, a parallelogram if and only if 
, and, by definition, a trapezoid if and only if 
. Since 
, the figure is a trapezoid with bases 
and 
and legs 
and 
. Since 
, the trapezoid is by definition an isosceles trapezoid.
Quadrilateral
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Find the area of the following trapezoid.
Find the area of the following trapezoid.
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The correct answer is 128 sq ft.
There are two ways to find the total area. One way to find the total area, you must find the area of the triangle and rectangle separately. After some deduction 
, you can find that the base of the triangle is 6 ft. Then using the Pythagorean Theorem, or 3-4-5 right triangles, you can find that the height of the triangle and rectangle is 8 ft. 
To find the area of the triangle, you would multiply 6 by 8 and then divide by 2 to get 24. To find the area of the rectangle, you would multiply 8 by 13 to get 104. Then you would add both areas to get 128 sq ft.
The other way to find the area is to use the formula for area of a trapezoid. After some deduction 
, you can find that the base of the triangle is 6ft. Then using the Pythagorean Theorem or 3-4-5 right triangles, you can find that the height of the triangle and rectangle is 8 ft.
Then you use the formula:
to get
The correct answer is 128 sq ft.
There are two ways to find the total area. One way to find the total area, you must find the area of the triangle and rectangle separately. After some deduction
To find the area of the triangle, you would multiply 6 by 8 and then divide by 2 to get 24. To find the area of the rectangle, you would multiply 8 by 13 to get 104. Then you would add both areas to get 128 sq ft.
The other way to find the area is to use the formula for area of a trapezoid. After some deduction
Then you use the formula:
to get
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A trapezoid has height 20 inches and area 640 square inches. Which of these choices can represent the lenghts of the two bases of the trapezoid?
A trapezoid has height 20 inches and area 640 square inches. Which of these choices can represent the lenghts of the two bases of the trapezoid?
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We can apply the area formula here.
The sum of the bases must be 64 inches. We check each one of these choices, except for 32 inches and 32 inches, which can be eliminated as the bases cannot be of the same length.
Only 27 and 37 have 64 as a sum, so this is the correct choice.
We can apply the area formula here.
The sum of the bases must be 64 inches. We check each one of these choices, except for 32 inches and 32 inches, which can be eliminated as the bases cannot be of the same length.
Only 27 and 37 have 64 as a sum, so this is the correct choice.
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