# SSAT Middle Level Math : Geometry

## Example Questions

### Example Question #1 : How To Find The Area Of A Square

What is the total area of the surface of the cube shown in the above diagram?

Explanation:

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:

### Example Question #8 : How To Find The Area Of A Figure

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?

Explanation:

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.

### Example Question #21 : Squares

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.

Explanation:

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.

### Example Question #21 : Quadrilaterals

The length of one side of a square is . What is the square's area?

Explanation:

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 .

### Example Question #4 : How To Find The Area Of A Square

If a square has a side that is 3 yards long, what is the area in square feet?

Explanation:

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.

### Example Question #101 : Geometry

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.

The correct answer is not given among the other choices.

Explanation:

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.

### Example Question #11 : How To Find The Area Of A Square

Find the area of a square with a width of 13cm.

Explanation:

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

### Example Question #1 : Rectangles

The width of a rectangle is half of its length.  If the width is given as what is the perimeter of the rectangle in terms of ?

Explanation:

The sum of the widths is and since the width is half the length, each length is Since there are 2 lengths we get a total perimeter of .

### Example Question #291 : Ssat Middle Level Quantitative (Math)

The above figure shows the size and shape of a yard that is to be surrounded by some fence. How many feet of fence will be needed?

Note: all sides meet at right angles.

Explanation:

The best way to see that 750 feet of fence are needed is to look at this augmented diagram.

Note that two of the sides are extended to form a smaller rectangle whose sides can be deduced by subtraction. Since opposite sides of a rectangle are congruent, this allows us to fill in the two missing sidelengths of the original figure.

### Example Question #3 : How To Find The Perimeter Of A Rectangle

Give the perimeter of the rectangle in the above diagram.