Quadrilaterals - SSAT Middle Level Quantitative
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The area of the square is 81. What is the sum of the lengths of three sides of the square?
The area of the square is 81. What is the sum of the lengths of three sides of the square?
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A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is 
.
A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is
What is the area of a square with perimeter 64 inches?
What is the area of a square with perimeter 64 inches?
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The perimeter of a square is four times its sidelength, so a square with perimeter 64 inches has sides with length 16 inches. Use the area formula:
The perimeter of a square is four times its sidelength, so a square with perimeter 64 inches has sides with length 16 inches. Use the area formula:
What is the total area of the surface of the cube shown in the above diagram?
What is the total area of the surface of the cube shown in the above diagram?
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A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:
Then multiply this by six:
A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:
Then multiply this by six:
What is the total area of the surface of the cube shown in the above diagram?
What is the total area of the surface of the cube shown in the above diagram?
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A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:
Then multiply this by six:
A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:
Then multiply this by six:
What is the total area of the surface of the cube shown in the above diagram?
What is the total area of the surface of the cube shown in the above diagram?
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A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:
Then multiply this by six:
A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:
Then multiply this by six:
What is the total area of the surface of the cube shown in the above diagram?
What is the total area of the surface of the cube shown in the above diagram?
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A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:
Then multiply this by six:
A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:
Then multiply this by six:
A square is 9 feet long on each side. How many smaller squares, each 3 feet on a side can be cut out of the larger square?
A square is 9 feet long on each side. How many smaller squares, each 3 feet on a side can be cut out of the larger square?
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Each side can be divided into three 3-foot sections. This gives a total of 
squares. Another way of looking at the problem is that the total area of the large square is 81 and each smaller square has an area of 9. Dividing 81 by 9 gives the correct answer.
Each side can be divided into three 3-foot sections. This gives a total of
Order the following from least area to greatest area:
Figure A: A square with sides of length 3 feet each.
Figure B: A rectangle with length 30 inches and width 42 inches.
Figure C: A rectangle with length 2 feet and width 4 feet.
Order the following from least area to greatest area:
Figure A: A square with sides of length 3 feet each.
Figure B: A rectangle with length 30 inches and width 42 inches.
Figure C: A rectangle with length 2 feet and width 4 feet.
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Figure A has area 
square feet.
Figure B has dimensions 
feet by 
feet, so its area is
square feet.
Figure C has area 
square feet.
From least area to greatest, the figures rank C, B, A.
Figure A has area
Figure B has dimensions
Figure C has area
From least area to greatest, the figures rank C, B, A.
The length of one side of a square is 
. What is the square's area?
The length of one side of a square is
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The area of any quadrilateral is found by multiplying the length by the width. Because a square has four equal sides, the length and width are the same. For the square in this question, the length and width are 
.
Remember: area is always given in units2 .
The area of any quadrilateral is found by multiplying the length by the width. Because a square has four equal sides, the length and width are the same. For the square in this question, the length and width are
Remember: area is always given in units2 .
If a square has a side that is 3 yards long, what is the area in square feet?
If a square has a side that is 3 yards long, what is the area in square feet?
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The area of a square is found by multiplying the length of a side by itself.
If one side is 3 yards, this means one side is 9 feet since there are 3 feet in a yard.
Since every side is of equal length, you would multiply 9 feet by 9 feet to find the area.
This results in 81 square feet, which is the correct answer.
The area of a square is found by multiplying the length of a side by itself.
If one side is 3 yards, this means one side is 9 feet since there are 3 feet in a yard.
Since every side is of equal length, you would multiply 9 feet by 9 feet to find the area.
This results in 81 square feet, which is the correct answer.
Note: Figure NOT drawn to scale.
Refer to the above diagram, which shows a square. Give the ratio of the area of the yellow region to that of the white region.
Note: Figure NOT drawn to scale.
Refer to the above diagram, which shows a square. Give the ratio of the area of the yellow region to that of the white region.
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The area of the entire square is the square of the length of a side, or
.
The area of the right triangle is half the product of its legs, or
.
The area of the yellow region is therefore the difference of the two, or
.
The ratio of the area of the yellow region to that of the white region is
; that is, 55 to 9.
The area of the entire square is the square of the length of a side, or
The area of the right triangle is half the product of its legs, or
The area of the yellow region is therefore the difference of the two, or
The ratio of the area of the yellow region to that of the white region is
Find the area of a square with a width of 13cm.
Find the area of a square with a width of 13cm.
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To find the area of a square, we will use the following formula:
where l is the length and w is the width of the square.
Now, we know the width of the square is 13cm. Because it is a square, all sides are equal. Therefore, the length is also 13cm.
So, we can substitute. We get
To find the area of a square, we will use the following formula:
where l is the length and w is the width of the square.
Now, we know the width of the square is 13cm. Because it is a square, all sides are equal. Therefore, the length is also 13cm.
So, we can substitute. We get
Florence wants to build a fence to surround her square garden. The garden has an area of 16 square yards. How much fencing will she need?
Florence wants to build a fence to surround her square garden. The garden has an area of 16 square yards. How much fencing will she need?
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So this question requires you to know the formula for area for a square which is side squared.
Thus, 
, so one side is the square root of 16, or 4.
To figure out the perimeter, add up all of the sides of the square which are all the same (4).
So this question requires you to know the formula for area for a square which is side squared.
Thus,
To figure out the perimeter, add up all of the sides of the square which are all the same (4).
A square has perimeter 89.4 centimeters. What is the length of one side?
A square has perimeter 89.4 centimeters. What is the length of one side?
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A square has four sides of equal measure, so divide its perimeter by 4:
A square has four sides of equal measure, so divide its perimeter by 4:
A square has perimeter 16 feet 4 inches. What is the length of one side?
A square has perimeter 16 feet 4 inches. What is the length of one side?
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One foot is equal to 12 inches, so the perimeter 16 feet 4 inches is equal to 
inches.
An square has four sides of equal measure, so divide its perimeter by 4:
To convert 49 inches to feet and inches:
One side measures 4 feet 1 inch.
One foot is equal to 12 inches, so the perimeter 16 feet 4 inches is equal to
An square has four sides of equal measure, so divide its perimeter by 4:
To convert 49 inches to feet and inches:
One side measures 4 feet 1 inch.
A sqaure has sides measuring 
inches. What is this square's perimeter?
A sqaure has sides measuring
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The perimeter of a shape is the distance around the outside boundry of that shape.
In order to find the perimeter, add up the lengths of the sides of that shape.
Because the sides of a square all have the same length, add 
. Equivalently, multiply the side length by the number of sides: 
.
Because perimeter measures length, the unit of the answer should be inches, not inches2.
The perimeter of a shape is the distance around the outside boundry of that shape.
In order to find the perimeter, add up the lengths of the sides of that shape.
Because the sides of a square all have the same length, add
Because perimeter measures length, the unit of the answer should be inches, not inches2.
The length of one side of a square is 
What is the perimeter of this square?
The length of one side of a square is
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The perimeter of a shape is the distance around the outside boundry of that shape.
In order to find the perimeter, add up the lengths of the sides of that shape.
Because a square has four equal sides, add 
to find the perimeter. Equivalently, multiply 
.
The perimeter of a shape is the distance around the outside boundry of that shape.
In order to find the perimeter, add up the lengths of the sides of that shape.
Because a square has four equal sides, add
Find the perimeter of the square in the figure.
Find the perimeter of the square in the figure.
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Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so:
top + right side + bottom + left side = perimeter.
Since a square has equal sides all around, we could also write the formulalike so:
The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:
For the this question, your work should then look like one of these two options:
or
Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so:
top + right side + bottom + left side = perimeter.
Since a square has equal sides all around, we could also write the formulalike so:
The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:
For the this question, your work should then look like one of these two options:
or
Find the perimeter of the square in the figure.
Find the perimeter of the square in the figure.
Tap to see back →
Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so:
top + right side + bottom + left side = perimeter.
Since a square has equal sides all around, we could also write the formulalike so:
The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:
For the this question, your work should then look like one of these two options:
or
Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so:
top + right side + bottom + left side = perimeter.
Since a square has equal sides all around, we could also write the formulalike so:
The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:
For the this question, your work should then look like one of these two options:
or
Find the perimeter of the square in the figure.
Find the perimeter of the square in the figure.
Tap to see back →
Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so:
top + right side + bottom + left side = perimeter.
Since a square has equal sides all around, we could also write the formulalike so:
The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:
For the this question, your work should then look like one of these two options:
or
Finding perimeter is easiest with squares. Perimeter is the distance around the outside of the figure. There are two good ways to find the perimeter. The first and longer method of finding perimeter is simply to add up the length of each side. Thus, we would take the length of top of the square and add it to the length of the right side. We'd continue all the way around. The formula for this method could be written like so:
top + right side + bottom + left side = perimeter.
Since a square has equal sides all around, we could also write the formulalike so:
The second and easier way of finding perimeter for a square is a simplification of the first method. Instead of adding the same number four times we could simply multiply by 4. Written as a formula, this would look like this:
For the this question, your work should then look like one of these two options:
or