Geometry - SSAT Middle Level Quantitative
Card 1 of 912
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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NOTE: Figure NOT drawn to scale.
What is the area of the parallelogram represented by the above figure?
NOTE: Figure NOT drawn to scale.
What is the area of the parallelogram represented by the above figure?
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The area of a parallelogram is its base multiplied by its height. The diagram below shows both in green:
The area of a parallelogram is its base multiplied by its height. The diagram below shows both in green:
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Find the area of the above parallelogram given a height of 5 units, as shown to scale.
Find the area of the above parallelogram given a height of 5 units, as shown to scale.
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Since the diagram is drawn to scale, the base of the parallelogram must be 6 units in length. Using the area formula for a parallelogram:
Since the diagram is drawn to scale, the base of the parallelogram must be 6 units in length. Using the area formula for a parallelogram:
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Given a base of 12 units and an area of 120 square units, find the height of the paralellogram shown above.
Given a base of 12 units and an area of 120 square units, find the height of the paralellogram shown above.
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The area formula for a parallelogram is:
Thus, to find the height, rearrange:
The area formula for a parallelogram is:
Thus, to find the height, rearrange:
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The above parallelogram has an area of 30 square units. Which of the following could be the lengths of the base and height of this figure? (Image not drawn to scale.)
The above parallelogram has an area of 30 square units. Which of the following could be the lengths of the base and height of this figure? (Image not drawn to scale.)
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The formula for the area of a parallelogram is:
Thus, the base and height must equal 30 square units when multiplied together.
3 and 10 are the only combination of base and height which, when multiplied, equal the area of 30 square units.
The formula for the area of a parallelogram is:
Thus, the base and height must equal 30 square units when multiplied together.
3 and 10 are the only combination of base and height which, when multiplied, equal the area of 30 square units.
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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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