Trapezoids - Geometry
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Find the area of a trapezoid with bases of 
and 
and a height of 
.
Find the area of a trapezoid with bases of
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The formula for the area of a trapezoid is:
Where 
and 
are the bases and 
is the height. Using this formula and the given values, we get:
The formula for the area of a trapezoid is:
Where
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.
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
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?
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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.
What is the area of the following trapezoid?
What is the area of the following trapezoid?
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The formula for the area of a trapezoid is:
,
where 
is the value of the top base, 
is value of the bottom base, and 
is the value 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:
Which of the following shapes is a trapezoid?
Which of the following shapes is a trapezoid?
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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.
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.
What is the area of the trapezoid pictured above in square units?
What is the area of the trapezoid pictured above in square units?
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The formula for the area of a trapezoid is the average of the bases times the height,
.
Looking at this problem and when the appropriate values are plugged in, the formula yields:
The formula for the area of a trapezoid is the average of the bases times the height,
Looking at this problem and when the appropriate values are plugged in, the formula yields:
What is the height of the trapezoid pictured above?
What is the height of the trapezoid pictured above?
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To find the height, we must introduce two variables, 
, each representing the bases of the triangles on the outside, so that 
. (Equation 1)
The next step is to set up two Pythagorean Theorems,
(Equation 2, 3)
The next step is a substitution from the first equation,
(Equation 4)
and plugging it in to the second equation, yielding
(Equation 5)
The next step is to substitute from Equation 3 into equation 5,
, 
which simplifies to
Once we have one of the bases, just plug into the Pythagorean Theorem, 
To find the height, we must introduce two variables,
The next step is to set up two Pythagorean Theorems,
The next step is a substitution from the first equation,
and plugging it in to the second equation, yielding
The next step is to substitute from Equation 3 into equation 5,
Once we have one of the bases, just plug into the Pythagorean Theorem,
A isosceles trapezoid with sides 
, 
, 
, and 
has a height of 
, what is the area?
A isosceles trapezoid with sides
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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:
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:
If the height of a trapezoid is 
, bottom base is 
, and the top base is 
, what is the area?
If the height of a trapezoid is
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The formula for finding the area of a trapezoid is:
Substitute the given values to find the area.
The formula for finding the area of a trapezoid is:
Substitute the given values to find the area.
Find the area of a trapezoid with bases of length 
and 
and a height of 
.
Find the area of a trapezoid with bases of length
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The formula for the area of a trapezoid is:
Where 
and 
are the bases and 
is the height. Using this formula and the given values, we get:
The formula for the area of a trapezoid is:
Where
Find the area of the above trapezoid.
Find the area of the above trapezoid.
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The formula for the area of a trapezoid is:
Where and are the bases and is the height. Using this formula and the given values, we get:
The formula for the area of a trapezoid is:
Where
Find the area of the above trapezoid.
Find the area of the above trapezoid.
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The formula for the area of a trapezoid is:
Where and are the bases and is the height. Using this formula and the given values, we get:
The formula for the area of a trapezoid is:
Where
Find the area of a trapezoid if the height is 
, and the small and large bases are 
and 
, respectively.
Find the area of a trapezoid if the height is
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Write the formula to find the area of a trapezoid.
Substitute the givens and evaluate the area.
Write the formula to find the area of a trapezoid.
Substitute the givens and evaluate the area.
The average of the lengths of the top and bottom of trapezoid
is 
What is the height of the trapezoid, if the area is 
?
The average of the lengths of the top and bottom of trapezoid
What is the height of the trapezoid, if the area is
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A right triangle and rectangle are placed adjacent to one another such that the composite figure formed by the triangle and rectangle is a trapezoid.
Find the area of the trapezoid given that the base of the triangle is 7 ft and the hypotenuse of the triangle is 25ft. The base of the rectangle is 9 feet.
A right triangle and rectangle are placed adjacent to one another such that the composite figure formed by the triangle and rectangle is a trapezoid.
Find the area of the trapezoid given that the base of the triangle is 7 ft and the hypotenuse of the triangle is 25ft. The base of the rectangle is 9 feet.
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Show algebraically how to develop the trapezoid area formula.
Show algebraically how to develop the trapezoid area formula.
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-
The area 
of the triangle that has base 
is 
.
-
The area 
of the triangle that has base 
is 
.
-
The sum of the two triangel areas is
-
The area
-
The area
-
The sum of the two triangel areas is
Find the area 
of the trapezoid.
Find the area
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- Using the trapezoid area formula,
,
height 
, base 
, base 
.
-
After substition, the resulting expression is 
.
-
The resulting expression is then simplified,
- Using the trapezoid area formula,
height
-
After substition, the resulting expression is
-
The resulting expression is then simplified,
Find the area of the shaded region.
Find the area of the shaded region.
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The shaded region is between the outer and inner trapezoid. To find the area of the shaded region, subtract the area of the inner trapezoid from the area of the outer trapezoid.
-
Area of the shaded region = 
, area of the outer trapezoid = 
, area of the inner trapezoid = 
.
-
, 
-
The shaded region is between the outer and inner trapezoid. To find the area of the shaded region, subtract the area of the inner trapezoid from the area of the outer trapezoid.
-
Area of the shaded region =
-
-
What is the area of this trapezoid?
What is the area of this trapezoid?
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The area of a trapezoid is
.
In this particular case the known values are as follows.
Substituting in the given values into the area formula we arrive at the following solution.
The area of a trapezoid is
In this particular case the known values are as follows.
Substituting in the given values into the area formula we arrive at the following solution.