All ISEE Lower Level Quantitative Resources
Example Questions
Example Question #1 : Geometry
The parallelogram shown above has a height of and a base of length
. Find the area of the parallelogram.
square units
square units
square units
square units
square units
To find the area of the parallelogram apply the formula:
Since, the paralleogram has a base of and a height of
the solution is:
Example Question #1 : How To Find A Parallelogram On A Coordinate Plane
The parallelogram shown above has a height of and a base of length
. Find the perimeter of the parallelogram.
In order to find the correct perimeter of the parallelogram apply the formula: , where
the length of one of the diagonal sides and
the length of the base.
In order to find the length of side , apply the formula:
. By drawing an altitude from point
to
, a right triangle is formed with a base that has a length of
and a height of
.
Thus, the solution is: length of side
Therefore,
Example Question #3 : How To Find A Parallelogram On A Coordinate Plane
Identify the coordinate points for the parallelogram that is shown above.
In order to identify the coordinate points for this parallelogram, notice that there must be two different pairs of coordinates with the same values.
Thus, the parallelogram has coordinate points:
Example Question #1 : How To Find A Parallelogram On A Coordinate Plane
What is the area of the parallelogram shown above?
square units
square units
square units
square units
square units
To find the area of the parallelogram that is shown, apply the formula:
Since the parallelogram has a base of and a height of
the solution is:
Example Question #1 : How To Find A Parallelogram On A Coordinate Plane
Given that the above parallelogram has base sides with a length of and diagonal sides with a length of
what is the perimeter of the parallelogram?
In order to find the perimeter of the parallelogram apply the formula: , where
the length of one diagonal side and
the length of one base.
In this problem, and
.
Thus, the correct answer is:
Example Question #1 : How To Find A Parallelogram On A Coordinate Plane
Identify the coordinate points for the parallelogram shown above.
In order to identify the coordinate points for this parallelogram, notice that there must be two different pairs of coordinates with the same values.
Thus, the correct set of coordinates is:
Example Question #1 : How To Find A Rectangle On A Coordinate Plane
A shape is plotted on a coordinate axis. The endpoints are . What shape is it?
Parallelogram
Rectangle
Square
Triangle
Trapezoid
Rectangle
Plot the points on a coordinate axis. Once it's graphed, you can see that there are two pairs of congruent, or equal, sides. The shape that best fits these characteristics is a rectangle.
Example Question #1 : How To Find A Rectangle On A Coordinate Plane
Rectangle has coordinates:
,
,
,
. Find the area of rectangle
.
square units
square units
square units
square units
square units
In order to find the area of rectangle apply the formula:
Since rectangle has a width of
and a length of
the solution is:
square units
Example Question #1 : How To Find A Rectangle On A Coordinate Plane
Rectangle has coordinates:
,
,
,
. What is the perimeter?
To find the perimeter of rectangle , apply the formula:
Thus, the solution is:
Example Question #1 : How To Find A Rectangle On A Coordinate Plane
Rectangle has coordinate points:
,
,
,
. Find the area of rectangle
.
square units
square units
square units
square units
square units
The area of rectangle can be found by multiplying the width and length of the rectangle.
To find the length of the rectangle compare the x values of two of the coordinates:
Since the length is
.
To find the width of the rectangle we need to look at the y coordinates of two of the points.
Since the width is
.
The solution is:
All ISEE Lower Level Quantitative Resources
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