How to find the area of a rectangle - ISEE Upper Level: Quantitative Reasoning
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Which is the greater quantity?
(a) The area of the rectangle on the coordinate plane with vertices 
(b) The area of the rectangle on the coordinate plane with vertices 
Which is the greater quantity?
(a) The area of the rectangle on the coordinate plane with vertices
(b) The area of the rectangle on the coordinate plane with vertices
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(a) The first rectangle has width 
and height 
; its area is 
.
(b) The second rectangle has width 
and height 
; its area is 
.
The areas of the rectangle are the same.
(a) The first rectangle has width
(b) The second rectangle has width
The areas of the rectangle are the same.
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. Which is the greater quantity?
(a) The area of the square on the coordinate plane with vertices 
(b) The area of the rectangle on the coordinate plane with vertices 
(a) The area of the square on the coordinate plane with vertices
(b) The area of the rectangle on the coordinate plane with vertices
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(a) The square has sidelength 
, and therefore has area 
.
(b) The rectangle has width 
and height 
, and therefore has area 
.
Since 
, the square in (a) has the greater area.
(a) The square has sidelength
(b) The rectangle has width
Since
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A rectangle on the coordinate plane has its vertices at the points 
.
Which is the greater quantity?
(a) The area of the portion of the rectangle in Quadrant I
(b) The area of the portion of the rectangle in Quadrant III
A rectangle on the coordinate plane has its vertices at the points
Which is the greater quantity?
(a) The area of the portion of the rectangle in Quadrant I
(b) The area of the portion of the rectangle in Quadrant III
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(a) The portion of the rectangle in Quadrant I is a rectangle with vertices 
, so its area is 
.
(a) The portion of the rectangle in Quadrant III is a rectangle with vertices 
, so its area is 
.
(a) The portion of the rectangle in Quadrant I is a rectangle with vertices
(a) The portion of the rectangle in Quadrant III is a rectangle with vertices
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The perimeter of a rectangle is one yard. The rectangle is three times as long as it is wide. Which is the greater quantity?
(a) The area of the rectangle
(b) 60 square inches
The perimeter of a rectangle is one yard. The rectangle is three times as long as it is wide. Which is the greater quantity?
(a) The area of the rectangle
(b) 60 square inches
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Let 
be the width of the rectangle. Then its length is 
, and its perimeter is
Since the perimeter is one yard, or 36 inches,
inches is the wiidth, and 
inches is the length, so the area is
square inches. (a) is the greater quantity.
Let
Since the perimeter is one yard, or 36 inches,
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If one rectangular park measures 
and another rectangular park measures 
, how many times greater is the area of the second park than the area of the first park?
If one rectangular park measures
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First, you must compute the area of both parks. The area of a rectangle is length times width. Therefore, the area of park one is 
, which is 
. The area of park two is 
, which is 
Then, divide the area of the second park by the area of the first park (
). This yields 3 as the answer.
First, you must compute the area of both parks. The area of a rectangle is length times width. Therefore, the area of park one is
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A rectangle is two feet shorter than twice its width; its perimeter is six yards. Give its area in square inches.
A rectangle is two feet shorter than twice its width; its perimeter is six yards. Give its area in square inches.
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The length of the rectangle is two feet, or 24 inches, shorter than twice the width, so, if 
is the width in inches, the length in inches is
Six yards, the perimeter of the rectangle, is equal to 
inches. The perimeter, in terms of length and width, is 
, so we can set up the equation:
The length and width are 64 inches and 44 inches; the area is their product, which is
square inches
The length of the rectangle is two feet, or 24 inches, shorter than twice the width, so, if
Six yards, the perimeter of the rectangle, is equal to
The length and width are 64 inches and 44 inches; the area is their product, which is
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The perimeter of a rectangle is 210 inches. The width of the rectangle is 40% of its length. What is the area of the rectangle?
The perimeter of a rectangle is 210 inches. The width of the rectangle is 40% of its length. What is the area of the rectangle?
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If the width of the rectangle is 40% of the length, then
.
The perimeter of the rectangle is:
The perimeter is 210 inches, so we can solve for the length:
The length and width of the rectangle are 75 and 30 inches; the area is their product, or
square inches.
If the width of the rectangle is 40% of the length, then
The perimeter of the rectangle is:
The perimeter is 210 inches, so we can solve for the length:
The length and width of the rectangle are 75 and 30 inches; the area is their product, or
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The sum of the lengths of three sides of a rectangle is 572 inches; the width of the rectangle is 60% of its length. Give its area in square inches.
The sum of the lengths of three sides of a rectangle is 572 inches; the width of the rectangle is 60% of its length. Give its area in square inches.
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Since the width of the rectangle is 60% of its length, we can write 
.
However, it is not clear from the problem which three sides - two lengths and a width or two widths and a length - we are choosing to have sum 572 inches. Depending on the three sides chosen, we can either set up
or
Since the length cannot be determined with certainty, neither can the width, and, subsequently, neither can the area.
Since the width of the rectangle is 60% of its length, we can write
However, it is not clear from the problem which three sides - two lengths and a width or two widths and a length - we are choosing to have sum 572 inches. Depending on the three sides chosen, we can either set up
or
Since the length cannot be determined with certainty, neither can the width, and, subsequently, neither can the area.
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Five rectangles each have the same length, which we will call 
. The widths of the five rectangles are 7, 5, 8, 10, and 12. Which of the following expressions is equal to the mean of their areas?
Five rectangles each have the same length, which we will call
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The area of a rectangle is the product of its width and its length. The areas of the five rectangles, therefore, are 
. The mean of these five areas is their sum divided by 5, or
The area of a rectangle is the product of its width and its length. The areas of the five rectangles, therefore, are
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Two rectangles, A and B, each have perimeter 32 feet. Rectangle A has length 12 feet; Rectangle B has length 10 feet. The area of Rectangle A is what percent of the area of Rectangle B?
Two rectangles, A and B, each have perimeter 32 feet. Rectangle A has length 12 feet; Rectangle B has length 10 feet. The area of Rectangle A is what percent of the area of Rectangle B?
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The perimeter of a rectangle can be given by the formula
Since for both rectangles, 30 is the perimeter, this becomes
, and subsequently
.
Rectangle A has length 12 feet and, subsequently. width 4 feet, making its area
square feet
Rectangle B has length 10 feet and, subsequently. width 6 feet, making its area
square feet
The area of Rectangle A is
of the area of Rectangle B.
The perimeter of a rectangle can be given by the formula
Since for both rectangles, 30 is the perimeter, this becomes
Rectangle A has length 12 feet and, subsequently. width 4 feet, making its area
Rectangle B has length 10 feet and, subsequently. width 6 feet, making its area
The area of Rectangle A is
of the area of Rectangle B.
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Give the area of the above rectangle in terms of 
.
Give the area of the above rectangle in terms of
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The area of a rectangle is equal to the product of its length and height, which here are 5 and 
. This product is 
.
The area of a rectangle is equal to the product of its length and height, which here are 5 and
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is a positive integer.
Rectangle A has length 
and width 
; Rectangle B has length 
and length 
. Which is the greater quantity?
(A) The area of Rectangle A
(B) The area of Rectangle B
Rectangle A has length
(A) The area of Rectangle A
(B) The area of Rectangle B
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This might be easier to solve if you set 
.
Then the dimensions of Rectangle A are 
and 
. The area of Rectangle A is their product:
The dimensions of Rectangle B are 
and 
. The area of Rectangle B is their product:
regardless of the value of 
(or, subsequently, 
), so Rectangle A has the greater area.
This might be easier to solve if you set
Then the dimensions of Rectangle A are
The dimensions of Rectangle B are
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In Rectangle 
, 
and 
. Give the area of this rectangle in terms of 
.
In Rectangle
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The area of a rectangle is the product of its length and its width, which here are 
and 
. Mulitply:
The area of a rectangle is the product of its length and its width, which here are
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Your geometry book has a rectangular front cover which is 12 inches by 8 inches.
What is the area of your book cover?
Your geometry book has a rectangular front cover which is 12 inches by 8 inches.
What is the area of your book cover?
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Your geometry book has a rectangular front cover which is 12 inches by 8 inches.
What is the area of your book cover?
To find the area of a rectangle, use the following formula:
Plug in our knowns and solve:
Your geometry book has a rectangular front cover which is 12 inches by 8 inches.
What is the area of your book cover?
To find the area of a rectangle, use the following formula:
Plug in our knowns and solve:
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A rectangle and a square have the same perimeter. The area of the square is 
square centimeters; the length of the rectangle is 
centimeters. Give the width of the rectangle in centimeters.
A rectangle and a square have the same perimeter. The area of the square is
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The sidelength of a square with area 
square centimeters is 
centimeters; its perimeter, as well as that of the rectangle, is therefore 
centimeters.
Using the formula for the perimeter of a rectangle, substitute 
and solve for 
as follows:
The sidelength of a square with area
Using the formula for the perimeter of a rectangle, substitute
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A rectangle on the coordinate plane has its vertices at the points .
What percent of the rectangle is located in Quadrant I?
A rectangle on the coordinate plane has its vertices at the points
What percent of the rectangle is located in Quadrant I?
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The total area of the rectangle is
.
The area of the portion of the rectangle in Quadrant I is
.
Therefore, the portion of the rectangle in Quadrant I is
.
The total area of the rectangle is
The area of the portion of the rectangle in Quadrant I is
Therefore, the portion of the rectangle in Quadrant I is
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In a rectangle, the width is 
while the length is 
. If 
, what is the area of the rectangle?
In a rectangle, the width is
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In a rectangle in which the width is x while the length is 4x, the first step is to solve for x. If 
, the value of x can be found by dividing each side of this equation by 3.
Doing so gives us the information that x is equal to 3.
Thus, the area is equal to:
In a rectangle in which the width is x while the length is 4x, the first step is to solve for x. If
Doing so gives us the information that x is equal to 3.
Thus, the area is equal to:
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Find the area of a rectangle with a width of 5in and a length that is three times the width.
Find the area of a rectangle with a width of 5in and a length that is three times the width.
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To find the area of a rectangle, we will use the following formula:
where l is the length and w is the width of the rectangle.
Now, we know the width of the rectangle is 5in. We also know the length is three times the width. Therefore, the length is 15in.
Knowing this, we can substitute into the formula. We get
To find the area of a rectangle, we will use the following formula:
where l is the length and w is the width of the rectangle.
Now, we know the width of the rectangle is 5in. We also know the length is three times the width. Therefore, the length is 15in.
Knowing this, we can substitute into the formula. We get
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Find the area of a rectangle with a width of 7cm and a length that is four times the width.
Find the area of a rectangle with a width of 7cm and a length that is four times the width.
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To find the area of a rectangle, we will use the following formula:
where l is the length and w is the width of the rectangle.
Now, we know the width of the rectangle is 7cm. We also know the length is four times the width. Therefore, the length is 28cm.
Knowing this, we will substitute into the formula. We get
To find the area of a rectangle, we will use the following formula:
where l is the length and w is the width of the rectangle.
Now, we know the width of the rectangle is 7cm. We also know the length is four times the width. Therefore, the length is 28cm.
Knowing this, we will substitute into the formula. We get
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Find the area of a rectangle with a width of 8cm and a length that is four times the width.
Find the area of a rectangle with a width of 8cm and a length that is four times the width.
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To find the area of a rectangle, we will use the following formula:
where l is the length and w is the width of the rectangle.
Now, we know the width of the rectangle is 8cm. We also know the length of the rectangle is four times the width. Therefore, the length of the rectangle is 32cm.
Knowing this, we will substitute into the formula. We get
To find the area of a rectangle, we will use the following formula:
where l is the length and w is the width of the rectangle.
Now, we know the width of the rectangle is 8cm. We also know the length of the rectangle is four times the width. Therefore, the length of the rectangle is 32cm.
Knowing this, we will substitute into the formula. We get
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