Trapezoids - ACT Math
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Find the measure of angle 
in the isosceles trapezoid pictured below.
Find the measure of angle
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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Given the following isosceles triangle:
In degrees, find the measure of the sum of 
and 
in the figure above.
Given the following isosceles triangle:
In degrees, find the measure of the sum of
All quadrilaterals' interior angles sum to 360°. In isosceles trapezoids, the two top angles are equal to each other.
Similarly, the two bottom angles are equal to each other as well.
Therefore, to find the sum of the two bottom angles, we subtract the measures of the top two angles from 360:
All quadrilaterals' interior angles sum to 360°. In isosceles trapezoids, the two top angles are equal to each other.
Similarly, the two bottom angles are equal to each other as well.
Therefore, to find the sum of the two bottom angles, we subtract the measures of the top two angles from 360:
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In the isosceles trapezoid above,
. 
and 
.
In degrees, what is the measure of 
?
In the isosceles trapezoid above,
In degrees, what is the measure of
To find the measure of angle DAC, we must know that the interior angles of all triangles sum up to 180 degrees. Also, as this is an isosceles trapezoid, 
and 
are equal to each other. The two diagonals within the trapezoid bisect angles 
and 
at the same angle.
Thus, 
must also be equal to 50 degrees.
Thus, 
.
Now that we know two angles out of the three in the triangle on the left, we can subtract them from 180 degrees to find 
:
To find the measure of angle DAC, we must know that the interior angles of all triangles sum up to 180 degrees. Also, as this is an isosceles trapezoid,
Thus,
Thus,
Now that we know two angles out of the three in the triangle on the left, we can subtract them from 180 degrees to find
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Trapezoid 
is an isosceles trapezoid with angle 
. If 
and 
are paired, what is the measure of 
?
Trapezoid
As a rule, adjacent (non-paired) angles in a trapezoid are supplementary. Thus, we know that if 
, then 
. Since we are told that 
and 
are paired and trapezoid 
is isosceles, 
must also equal 
.
As a rule, adjacent (non-paired) angles in a trapezoid are supplementary. Thus, we know that if
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What is the area of this regular trapezoid?
What is the area of this regular trapezoid?
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?
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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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
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.
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Trapezoid 
has an area of 
. If height 
and 
, what is the measure of 
?
Trapezoid
The formula for the area of a trapezoid is:
We have here the height and one of the bases, plus the area, and we are being asked to find the length of base 
. Plug in known values and solve.
Thus, 
The formula for the area of a trapezoid is:
We have here the height and one of the bases, plus the area, and we are being asked to find the length of base
Thus,
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Find the area of a trapezoid given bases of length 6 and 7 and height of 2.
Find the area of a trapezoid given bases of length 6 and 7 and height of 2.
To solve, simply use the formula for the area of a trapezoid.
Substitute
into the area formula.
Thus,
To solve, simply use the formula for the area of a trapezoid.
Substitute
into the area formula.
Thus,
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Given the height of a trapezoid is 
and a base length is 
, what is the length of the other base if the area of the trapezoid is 
?
Given the height of a trapezoid is
Write the formula used to find the area of a trapezoid.
Substitute the given information to the formula and solve for the unknown base.
Write the formula used to find the area of a trapezoid.
Substitute the given information to the formula and solve for the unknown base.
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is an isosceles trapezoid that is bisected by 
.
. If 
, 
, and 
, then what is the length of 
?
We know that all three horizontal lines are parallel to one another. By definition, we can set up a ratio between the lengths of the sides provided to us in the question and the lengths of the two parallel lines:
Once we substitute the given information, we get
We cross multiply to solve for EF
We know that all three horizontal lines are parallel to one another. By definition, we can set up a ratio between the lengths of the sides provided to us in the question and the lengths of the two parallel lines:
Once we substitute the given information, we get
We cross multiply to solve for EF
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Find the measure of angle in the isosceles trapezoid pictured below.
Find the measure of angle
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**°**.
Compare your answer with the correct one above
Given the following isosceles triangle:
In degrees, find the measure of the sum of and in the figure above.
Given the following isosceles triangle:
In degrees, find the measure of the sum of
All quadrilaterals' interior angles sum to 360°. In isosceles trapezoids, the two top angles are equal to each other.
Similarly, the two bottom angles are equal to each other as well.
Therefore, to find the sum of the two bottom angles, we subtract the measures of the top two angles from 360:
All quadrilaterals' interior angles sum to 360°. In isosceles trapezoids, the two top angles are equal to each other.
Similarly, the two bottom angles are equal to each other as well.
Therefore, to find the sum of the two bottom angles, we subtract the measures of the top two angles from 360:
Compare your answer with the correct one above
In the isosceles trapezoid above,
. and .
In degrees, what is the measure of ?
In the isosceles trapezoid above,
In degrees, what is the measure of
To find the measure of angle DAC, we must know that the interior angles of all triangles sum up to 180 degrees. Also, as this is an isosceles trapezoid, and are equal to each other. The two diagonals within the trapezoid bisect angles and at the same angle.
Thus, must also be equal to 50 degrees.
Thus, .
Now that we know two angles out of the three in the triangle on the left, we can subtract them from 180 degrees to find :
To find the measure of angle DAC, we must know that the interior angles of all triangles sum up to 180 degrees. Also, as this is an isosceles trapezoid,
Thus,
Thus,
Now that we know two angles out of the three in the triangle on the left, we can subtract them from 180 degrees to find
Compare your answer with the correct one above
Trapezoid is an isosceles trapezoid with angle . If and are paired, what is the measure of ?
Trapezoid
As a rule, adjacent (non-paired) angles in a trapezoid are supplementary. Thus, we know that if , then . Since we are told that and are paired and trapezoid is isosceles, must also equal .
As a rule, adjacent (non-paired) angles in a trapezoid are supplementary. Thus, we know that if
Compare your answer with the correct one above
What is the area of this regular trapezoid?
What is the area of this regular trapezoid?
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.
Compare your answer with the correct one above
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?
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
Compare your answer with the correct one above
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
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.
Compare your answer with the correct one above
Trapezoid has an area of . If height and , what is the measure of ?
Trapezoid
The formula for the area of a trapezoid is:
We have here the height and one of the bases, plus the area, and we are being asked to find the length of base . Plug in known values and solve.
Thus,
The formula for the area of a trapezoid is:
We have here the height and one of the bases, plus the area, and we are being asked to find the length of base
Thus,
Compare your answer with the correct one above
Find the area of a trapezoid given bases of length 6 and 7 and height of 2.
Find the area of a trapezoid given bases of length 6 and 7 and height of 2.
To solve, simply use the formula for the area of a trapezoid.
Substitute
into the area formula.
Thus,
To solve, simply use the formula for the area of a trapezoid.
Substitute
into the area formula.
Thus,
Compare your answer with the correct one above