How to find the area of a square - SSAT Middle Level Quantitative

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:

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 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:

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.

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.

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 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 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.

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

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 .

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:

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 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:

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.

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.