Plane Geometry - ISEE Middle Level Quantitative Reasoning
Card 0 of 2680
The area of a square is 
?
The area of a square is
The area of a square is the side length squared not the side length times 
.
The area of a square is the side length squared not the side length times
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If you are given one side length of a square, you can find the area with that information.
If you are given one side length of a square, you can find the area with that information.
To find the area of a square, you multiple 
. But with a square all the sides are equal so the equation really is 
or the side length squared. Since you are given the side length, you can find the area.
To find the area of a square, you multiple
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Each side of a square is 
units long. Which is the greater quantity?
(A) The area of the square
(B) 
Each side of a square is
(A) The area of the square
(B)
The area of a square is the square of its side length:
Using the side length from the question:
However, it is impossible to tell with certainty which of 
and 
is greater.
For example, if 
,
and
so 
if .
But if 
,
and
so 
if .
The area of a square is the square of its side length:
Using the side length from the question:
However, it is impossible to tell with certainty which of
For example, if
and
so
But if
and
so
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What is the perimeter of a square with area 196 square inches?
What is the perimeter of a square with area 196 square inches?
A square with area 196 square inches has sidelength 
inches, and therefore has perimeter 
inches
A square with area 196 square inches has sidelength
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If a square has sides measuring 
, what is the perimeter of the square, in simplest form?
If a square has sides measuring
To find the perimeter of a square, you must add together all the sides. In this case, we are adding 
four times.
Since all of the denominators are the same, there is no need to find a commond denominator, so we add together the numerators. This gives us 
.
Since both the numerator and denomator are divisible by four, we must simplify this fraction.
The perimeter of the square is 
.
To find the perimeter of a square, you must add together all the sides. In this case, we are adding
Since all of the denominators are the same, there is no need to find a commond denominator, so we add together the numerators. This gives us
Since both the numerator and denomator are divisible by four, we must simplify this fraction.
The perimeter of the square is
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The sum of the lengths of three sides of a square is one foot. Give the perimeter of the square in inches.
The sum of the lengths of three sides of a square is one foot. Give the perimeter of the square in inches.
A square has four sides of the same length.
One foot is equal to twelve inches; since the sum of the lengths of three of the congruent sides is twelve inches, each side measures
inches.
The perimeter is
inches.
A square has four sides of the same length.
One foot is equal to twelve inches; since the sum of the lengths of three of the congruent sides is twelve inches, each side measures
The perimeter is
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A square has perimeter one yard. Which is the greater quantity?
(A) The length of one side of the square
(B) 8 inches
A square has perimeter one yard. Which is the greater quantity?
(A) The length of one side of the square
(B) 8 inches
One yard is equal to 36 inches. A square has four sides of equal length, so one side of the square has length
inches.
Since 
, (A) is greater.
One yard is equal to 36 inches. A square has four sides of equal length, so one side of the square has length
Since
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A square has perimeter five meters. Which is the greater quantity?
(A) 1,250 millimeters
(B) The length of one side of the square
A square has perimeter five meters. Which is the greater quantity?
(A) 1,250 millimeters
(B) The length of one side of the square
One meter is equal to 1,000 millimeters, so the square has perimeter
millimeters.
A square has four sides of equal length, so one side of the square has length
millimeters.
The quantities are equal.
One meter is equal to 1,000 millimeters, so the square has perimeter
A square has four sides of equal length, so one side of the square has length
The quantities are equal.
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A square has perimeter one meter. Which is the greater quantity?
(A) 250 centimeters
(B) The length of one side of the square
A square has perimeter one meter. Which is the greater quantity?
(A) 250 centimeters
(B) The length of one side of the square
One meter is equal to 100 centimeters.
A square has four sides of equal length, so we will need to divide by 4 to find the length of one side.
, so (A) is greater
One meter is equal to 100 centimeters.
A square has four sides of equal length, so we will need to divide by 4 to find the length of one side.
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A square lot has perimeter one mile. Which is the greater quantity?
(A) 1,320 feet
(B) The length of one side of the square
A square lot has perimeter one mile. Which is the greater quantity?
(A) 1,320 feet
(B) The length of one side of the square
One mile is equal to 5,280 feet. A square has four sides of equal length, so one side of the square has length
feet.
The quantities are equal.
One mile is equal to 5,280 feet. A square has four sides of equal length, so one side of the square has length
The quantities are equal.
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Each side of a square is 
units long. Which is the greater quantity?
(A) 
(B) The perimeter of the square
Each side of a square is
(A)
(B) The perimeter of the square
The perimeter of a square is four times its side length:
Since the perimeter is equal to , (A) and (B) are equal.
The perimeter of a square is four times its side length:
Since the perimeter is equal to
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The sum of the lengths of three sides of a square is 9,000 centimeters. Give its perimeter in meters.
The sum of the lengths of three sides of a square is 9,000 centimeters. Give its perimeter in meters.
100 centimeters are equal to one meter, so 9,000 centimeters are equal to
meters.
A square has four sides of the same length. Since the sum of the lengths of three of the congruent sides is 9,000 centimeters, or 90 meters, each side measures
meters.
The perimeter is four times this, which is
meters.
100 centimeters are equal to one meter, so 9,000 centimeters are equal to
A square has four sides of the same length. Since the sum of the lengths of three of the congruent sides is 9,000 centimeters, or 90 meters, each side measures
The perimeter is four times this, which is
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What is the length of a rectangular room with a perimeter of 
and a width of 
What is the length of a rectangular room with a perimeter of
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract 
from both sides
Divide 
by both sides
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract
Divide
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What is the length of a rectangular room with a perimeter of 
and a width of 
What is the length of a rectangular room with a perimeter of
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract 
from both sides
Divide 
by both sides
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract
Divide
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What is the length of a rectangular room with a perimeter of 
and a width of 
What is the length of a rectangular room with a perimeter of
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract 
from both sides
Divide 
by both sides
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract
Divide
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What is the length of a rectangular room with a perimeter of 
and a width of 
What is the length of a rectangular room with a perimeter of
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract 
from both sides
Divide 
by both sides
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract
Divide
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What is the length of a rectangular room with a perimeter of 
and a width of 
What is the length of a rectangular room with a perimeter of
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract 
from both sides
Divide 
by both sides
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract
Divide
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What is the length of a rectangular room with a perimeter of 
and a width of 
What is the length of a rectangular room with a perimeter of
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract 
from both sides
Divide 
by both sides
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract
Divide
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What is the length of a rectangular room with a perimeter of 
and a width of 
What is the length of a rectangular room with a perimeter of
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract 
from both sides
Divide 
by both sides
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract
Divide
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What is the area of the figure below?
What is the area of the figure below?
To find the area of the figure above, we need to slip the figure into two rectangles.
Using our area formula, 
, we can solve for the area of both of our rectangles
To find our final answer, we need to add the areas together.
To find the area of the figure above, we need to slip the figure into two rectangles.
Using our area formula,
To find our final answer, we need to add the areas together.
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