Coordinate Geometry - SSAT Middle Level Quantitative
Card 1 of 168
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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Find the area of the above square.
Find the area of the above square.
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In order to find the area of the square above apply the formula: 
, where 
the length of one side of the square.
Since 
,
the solution is 
In order to find the area of the square above apply the formula:
Since
the solution is
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Find the perimeter of the square shown above.
Find the perimeter of the square shown above.
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To find the perimeter of this square, apply the formula: 
, where 
the length of one side of the square.
Thus, the solution is:
To find the perimeter of this square, apply the formula:
Thus, the solution is:
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If a square has an area of 
square units, what is the perimeter?
If a square has an area of
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In order to solve this problem, apply the formula 
, in order to conclude that the length of side 
must equal 
for the area to equal 
.
Once you've found the length of side 
, apply the formula 
.
Thus, the solution is 
In order to solve this problem, apply the formula
Once you've found the length of side
Thus, the solution is
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A square has an area of 
square units, what is the perimeter?
A square has an area of
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In order to solve this problem, apply the formula 
, in order to conclude that the length of side 
must equal 
for the area to equal 
.
Once you've found the length of side 
, apply the formula 
In order to solve this problem, apply the formula
Once you've found the length of side
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A square has an area of 
square units, what is the perimeter of the square?
A square has an area of
Tap to reveal answer
In order to solve this problem, apply the formula 
, in order to conclude that the length of side 
must equal 
for the area to equal 
.
Once you've found the length of side 
, apply the formula 
In order to solve this problem, apply the formula
Once you've found the length of side
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A square has an area of 
square units. Find the perimeter.
A square has an area of
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In order to solve this problem, apply the formula 
, in order to conclude that the length of side 
must equal 
for the area to equal 
.
Once you've found the length of side 
, apply the formula 
In order to solve this problem, apply the formula
Once you've found the length of side
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Find the area of the square shown above.
Find the area of the square shown above.
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In order to find the area of the above square, apply the formula: 
, when 
equals the length of one side of the square.
Since, 
the solution is:
Make sure to attach "square units" to your answer!
In order to find the area of the above square, apply the formula:
Since,
Make sure to attach "square units" to your answer!
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The above square has an area of 
square units. What fraction of the area of square is in quadrant II?
The above square has an area of
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To find the fraction of the entire squares area that lays in quadrant II, notice that the square is taking up an equivalent amount in each of the four quadrants. Thus, 
of the squares area is in quadrant II.
Also note that the area of the square that lays in quadrant II is 
square units, thus the problem could have alternatively been solved by reducing 
.
To find the fraction of the entire squares area that lays in quadrant II, notice that the square is taking up an equivalent amount in each of the four quadrants. Thus,
Also note that the area of the square that lays in quadrant II is
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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?
Tap to reveal answer
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.
Tap to reveal answer
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.
Tap to reveal answer
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.)
Tap to reveal answer
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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Find the area of the above triangle, given that it has a height of 12 and a base of 10.
Find the area of the above triangle, given that it has a height of 12 and a base of 10.
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Because this is a right triangle, the area formula is simply:
Thus, the solution is:
Because this is a right triangle, the area formula is simply:
Thus, the solution is:
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Given the above triangle has a base of 5 and height of 6, what is the perimeter of the triangle?
Given the above triangle has a base of 5 and height of 6, what is the perimeter of the triangle?
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First, use the Pythagorean Theorem to find the length of the hypotenuse:
where 
and 
are 5 and 6, respectively, and 
is the hypotenuse.
Thus, 
Finally, the perimeter is the sum of the sides of the triangle or:
First, use the Pythagorean Theorem to find the length of the hypotenuse:
Thus,
Finally, the perimeter is the sum of the sides of the triangle or:
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Given the above triangle has a base of 
and hypotenuse of 
, find the height of the triangle.
Given the above triangle has a base of
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Use the Pythagorean Theorem,
where 
is the hypotenuse, 
is the base, and 
is the height.
Rearranging to solve for the height, 
, yields:
Use the Pythagorean Theorem,
where
Rearranging to solve for the height,
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Given triangle 
, where 
is at point 
and 
is at point 
, find the area.
Given triangle
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To find the area of this triangle, we first need to determine the length of sides AB and BC. First, point B shares the same x-coordinate as point A and the same y-coordinate as point C. Thus, B must be located at point (-2,-2).
The length of side AB must then be:
and the length of side BC:
Using the area formula,
we can find the area using the base (side BC) and height (side AB):
To find the area of this triangle, we first need to determine the length of sides AB and BC. First, point B shares the same x-coordinate as point A and the same y-coordinate as point C. Thus, B must be located at point (-2,-2).
The length of side AB must then be:
and the length of side BC:
Using the area formula,
we can find the area using the base (side BC) and height (side AB):
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