Plane Geometry - SSAT Middle Level Quantitative
Card 1 of 744
Note: Figure NOT drawn to scale
In the above diagram, 
Give the area of the parallelogram.
Note: Figure NOT drawn to scale
In the above diagram,
Give the area of the parallelogram.
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The area of a parallelogram is its base multiplied by its height - represented by 
and 
here:
Note that the value of 
is irrelevant.
The area of a parallelogram is its base multiplied by its height - represented by
Note that the value of
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Find the area of the following parallelogram:
Note: The formula for the area of a parallelogram is 
.
Find the area of the following parallelogram:
Note: The formula for the area of a parallelogram is
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The base of the parallelogram is 10, while the height is 5.
The base of the parallelogram is 10, while the height is 5.
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Find the area:
Find the area:
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The area of a parallelogram can be determined using the following equation:
Therefore,
The area of a parallelogram can be determined using the following equation:
Therefore,
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Find the area of the given parallelogram if 
.
Find the area of the given parallelogram if
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In order to find the area of a parallelogram, we need to find the product of the base length and height.
Notice that only two of the given values were needed to slove this problem.
In order to find the area of a parallelogram, we need to find the product of the base length and height.
Notice that only two of the given values were needed to slove this problem.
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A given parallelogram has a base 
in length, a height 
in length, and a side of length 
opposite the height. What is the area of the parallelogram?
A given parallelogram has a base
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The formula for the area of a parallelogram is 
, with base and height represented by 
and 
, respectively. Substituting values from the question:
The formula for the area of a parallelogram is
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A parallelogram has a height of 
in length, a side of length 
opposite the height, and a base of 
. What is the area of the parallelogram?
A parallelogram has a height of
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Given base 
and height 
, 
.
Substituting the values from our question:
Given base
Substituting the values from our question:
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A parallelogram has a base of length 
, a height of length 
, and a side of length 
. What is the area of the parallelogram?
A parallelogram has a base of length
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Given base and height , .
Substituting the values from our question:
Given base
Substituting the values from our question:
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Find the area of a parallelogram with a height of 
, a base of 
, and a side length of 
.
Find the area of a parallelogram with a height of
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The area 
of a parallelogram with height 
and base 
can be found with the equation 
. Consequently:
The area
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Find the area of a parallelogram with a height of 
, base of 
, and a side length of 
.
Find the area of a parallelogram with a height of
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The area 
of a parallelogram with height 
and base 
can be found with the equation 
. Consequently:
The area
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A triangle has sides 
feet, 
feet, and 
feet. Calculate its perimeter.
A triangle has sides
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The perimeter of any figure is the sum of the lengths of the sides: 
.
The perimeter of any figure is the sum of the lengths of the sides:
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Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?
Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?
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An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.
This makes the perimeter either
or
Of our choices, we choose 38.
An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.
This makes the perimeter either
or
Of our choices, we choose 38.
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The perimeter of an isosceles triangle is 18. What is a possible list of the lengths of the sides?
The perimeter of an isosceles triangle is 18. What is a possible list of the lengths of the sides?
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Since it is isosceles, 2 of the sides must be equal. They must also add to 18.
Since it is isosceles, 2 of the sides must be equal. They must also add to 18.
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An equilateral triangle has perimeter 
centimeters. How long is one side?
An equilateral triangle has perimeter
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An equilateral triangle has three sides of equal measure, so divide its perimeter by 
:
An equilateral triangle has three sides of equal measure, so divide its perimeter by
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An equilateral triangle has perimeter 8 feet 6 inches. How long is one side?
An equilateral triangle has perimeter 8 feet 6 inches. How long is one side?
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One foot is equal to 12 inches, so the perimeter 8 feet 6 inches is equal to 
inches.
An equilateral triangle has three sides of equal measure, so divide its perimeter by 3:
To convert 34 inches to feet and inches:
One side measures 2 feet 10 inches.
One foot is equal to 12 inches, so the perimeter 8 feet 6 inches is equal to
An equilateral triangle has three sides of equal measure, so divide its perimeter by 3:
To convert 34 inches to feet and inches:
One side measures 2 feet 10 inches.
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A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?
A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?
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By the Pythagorean Theorem, if 
and 
are the legs of a right triangle and 
is its hypotenuse, then
.
Set 
and solve for 
:
The perimeter of the triangle - the sum of the sidelengths - is
.
By the Pythagorean Theorem, if
Set
The perimeter of the triangle - the sum of the sidelengths - is
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Find the perimeter of the triangle above.
Note: Figure not drawn to scale.
Find the perimeter of the triangle above.
Note: Figure not drawn to scale.
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The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides: 
.
Because the lengths are in inches, the answer must be in inches as well.
The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides:
Because the lengths are in inches, the answer must be in inches as well.
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What is the perimeter of an equilateral triangle with a side length 
?
What is the perimeter of an equilateral triangle with a side length
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The perimeter is equal to the sum of the length of the sides. An equilateral triangle has three sides with equal lengths.
The perimeter is equal to the sum of the length of the sides. An equilateral triangle has three sides with equal lengths.
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A right triangle has legs 
feet and 
feet long. What is its perimeter, in inches?
A right triangle has legs
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The length of the hypotenuse of the triangle can be found using the Pythagorean Theorem. Substitute 
:
feet
Its perimeter is 
feet. Multiply by 12 to get the perimeter in inches:
inches
The length of the hypotenuse of the triangle can be found using the Pythagorean Theorem. Substitute
Its perimeter is
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If the triangle below is an isosceles triangle, what of the following choices could be its perimeter?
If the triangle below is an isosceles triangle, what of the following choices could be its perimeter?
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An isosceles triangle has 2 equal sides and a third side that is unequal. If one given side is 5 and the other is 7, then the third missing side must equal either 5 or 7. If the missing side has length 5, then the perimeter is 17 (5+5+7). If the missing side is of length 7, then the perimeter is 19 (7+7+5). Of the two, only 19 is an answer choice, so the correct answer is 19.
An isosceles triangle has 2 equal sides and a third side that is unequal. If one given side is 5 and the other is 7, then the third missing side must equal either 5 or 7. If the missing side has length 5, then the perimeter is 17 (5+5+7). If the missing side is of length 7, then the perimeter is 19 (7+7+5). Of the two, only 19 is an answer choice, so the correct answer is 19.
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The perimeter of equilateral triangle QRS is 4 times the perimeter of equilateral triangle TUV. If the perimeter of QRS is 36, what is the length of one side of TUV?
The perimeter of equilateral triangle QRS is 4 times the perimeter of equilateral triangle TUV. If the perimeter of QRS is 36, what is the length of one side of TUV?
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If the perimeter of QRS is 4 times the perimeter of TUV, and the perimeter of QRS is 36, then the perimeter of TUV is equal to 36 divided by 4, which is 9. If the perimeter of equilateral triangle TUV is 9, then each individual side must have length 3.
If the perimeter of QRS is 4 times the perimeter of TUV, and the perimeter of QRS is 36, then the perimeter of TUV is equal to 36 divided by 4, which is 9. If the perimeter of equilateral triangle TUV is 9, then each individual side must have length 3.
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