Trapezoids - ISEE Upper Level Quantitative Reasoning
Card 0 of 36
Find the area of the above trapezoid if 
, 
, and 
.
Figure not drawn to scale.
Find the area of the above trapezoid if
Figure not drawn to scale.
The area of a trapezoid is given by
,
where 
, 
are the lengths of each base and 
is the altitude (height) of the trapezoid.
The area of a trapezoid is given by
where
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A trapezoid has the base lengths of 
and 
. The area of the trapezoid is 
. Give the height of the trapezoid in terms of 
.
A trapezoid has the base lengths of
The area of a trapezoid is given by
,
where 
, 
are the lengths of each base and 
is the altitude (height) of the trapezoid.
The area of a trapezoid is given by
where
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In the following trapezoid 
and 
. The area of the trapezoid is 54 square inches. Give the height of the trapezoid. Figure not drawn to scale.
In the following trapezoid
The area of a trapezoid is given by
,
where 
, 
are the lengths of each base and 
is the altitude (height) of the trapezoid.
Substitute these values into the area formula:
The area of a trapezoid is given by
where
Substitute these values into the area formula:
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Note: Figure NOT drawn to scale.
The above trapezoid has area 
. What is 
?
Note: Figure NOT drawn to scale.
The above trapezoid has area
Substitute 
in the formula for the area of a trapezoid:
Substitute
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A trapezoid has height 20 inches. Its bases have sum 30 inches, and one base is 6 inches longer than the other. What is the area of this trapezoid?
A trapezoid has height 20 inches. Its bases have sum 30 inches, and one base is 6 inches longer than the other. What is the area of this trapezoid?
You do not need to find the individual bases; their sum, 
, is 
. You can substitute 
into the formula for the area of a trapezoid:
square inches.
Note that the fact that one base is 
inches longer is not important here.
You do not need to find the individual bases; their sum,
Note that the fact that one base is
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What is the area of the shaded portion of the above square?
What is the area of the shaded portion of the above square?
Quadrilateral 
- the shaded region - is a trapezoid with bases 
and 
, and altitude 
. The area of the trapezoid can be calculated using the formula
,
where 
and 
, and 
.
The length of 
can be found by setting 
and 
and applying the Pythagorean Theorem:
Therefore,
.
Substituting:
Quadrilateral
where
The length of
Therefore,
Substituting:
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Note: Figure NOT drawn to scale.
The area of the above trapezoid is 
. What is 
?
Note: Figure NOT drawn to scale.
The area of the above trapezoid is
Substitute 
into the formula for the area of a trapezoid:
Substitute
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The perimeter of the following trapezoid is 
.
The following is given:
Find 
.
Figure not drawn to scale.
The perimeter of the following trapezoid is
The following is given:
Find
Figure not drawn to scale.
The perimeter of a trapezoid is equal to the sum of all of the sides, i.e.
,
where 
are the lengths of each side.
The perimeter of a trapezoid is equal to the sum of all of the sides, i.e.
where
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The bigger base length of a trapezoid is two times bigger than the smaller base length. Legs of the trapezoid have the same length of 
. If the perimeter of the trapezoid is 
, give the length of the smaller base.
The bigger base length of a trapezoid is two times bigger than the smaller base length. Legs of the trapezoid have the same length of
Like any polygon, the perimeter of a trapezoid is the total distance around the outside, i.e.
,
where 
are the lengths of each side.
Let 
small base length and 
big base length.
Like any polygon, the perimeter of a trapezoid is the total distance around the outside, i.e.
where
Let
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Find the area of the above trapezoid if , , and .
Figure not drawn to scale.
Find the area of the above trapezoid if
Figure not drawn to scale.
The area of a trapezoid is given by
,
where , are the lengths of each base and is the altitude (height) of the trapezoid.
The area of a trapezoid is given by
where
Compare your answer with the correct one above
A trapezoid has the base lengths of and . The area of the trapezoid is . Give the height of the trapezoid in terms of .
A trapezoid has the base lengths of
The area of a trapezoid is given by
,
where , are the lengths of each base and is the altitude (height) of the trapezoid.
The area of a trapezoid is given by
where
Compare your answer with the correct one above
In the following trapezoid and . The area of the trapezoid is 54 square inches. Give the height of the trapezoid. Figure not drawn to scale.
In the following trapezoid
The area of a trapezoid is given by
,
where , are the lengths of each base and is the altitude (height) of the trapezoid.
Substitute these values into the area formula:
The area of a trapezoid is given by
where
Substitute these values into the area formula:
Compare your answer with the correct one above
Note: Figure NOT drawn to scale.
The above trapezoid has area . What is ?
Note: Figure NOT drawn to scale.
The above trapezoid has area
Substitute in the formula for the area of a trapezoid:
Substitute
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A trapezoid has height 20 inches. Its bases have sum 30 inches, and one base is 6 inches longer than the other. What is the area of this trapezoid?
A trapezoid has height 20 inches. Its bases have sum 30 inches, and one base is 6 inches longer than the other. What is the area of this trapezoid?
You do not need to find the individual bases; their sum, , is . You can substitute into the formula for the area of a trapezoid:
square inches.
Note that the fact that one base is inches longer is not important here.
You do not need to find the individual bases; their sum,
Note that the fact that one base is
Compare your answer with the correct one above
What is the area of the shaded portion of the above square?
What is the area of the shaded portion of the above square?
Quadrilateral - the shaded region - is a trapezoid with bases and , and altitude . The area of the trapezoid can be calculated using the formula
,
where and , and .
The length of can be found by setting and and applying the Pythagorean Theorem:
Therefore,
.
Substituting:
Quadrilateral
where
The length of
Therefore,
Substituting:
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Note: Figure NOT drawn to scale.
The area of the above trapezoid is . What is ?
Note: Figure NOT drawn to scale.
The area of the above trapezoid is
Substitute into the formula for the area of a trapezoid:
Substitute
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The perimeter of the following trapezoid is .
The following is given:
Find .
Figure not drawn to scale.
The perimeter of the following trapezoid is
The following is given:
Find
Figure not drawn to scale.
The perimeter of a trapezoid is equal to the sum of all of the sides, i.e.
,
where are the lengths of each side.
The perimeter of a trapezoid is equal to the sum of all of the sides, i.e.
where
Compare your answer with the correct one above
The bigger base length of a trapezoid is two times bigger than the smaller base length. Legs of the trapezoid have the same length of . If the perimeter of the trapezoid is , give the length of the smaller base.
The bigger base length of a trapezoid is two times bigger than the smaller base length. Legs of the trapezoid have the same length of
Like any polygon, the perimeter of a trapezoid is the total distance around the outside, i.e.
,
where are the lengths of each side.
Let small base length and big base length.
Like any polygon, the perimeter of a trapezoid is the total distance around the outside, i.e.
where
Let
Compare your answer with the correct one above
Find the area of the above trapezoid if , , and .
Figure not drawn to scale.
Find the area of the above trapezoid if
Figure not drawn to scale.
The area of a trapezoid is given by
,
where , are the lengths of each base and is the altitude (height) of the trapezoid.
The area of a trapezoid is given by
where
Compare your answer with the correct one above
A trapezoid has the base lengths of and . The area of the trapezoid is . Give the height of the trapezoid in terms of .
A trapezoid has the base lengths of
The area of a trapezoid is given by
,
where , are the lengths of each base and is the altitude (height) of the trapezoid.
The area of a trapezoid is given by
where
Compare your answer with the correct one above