SSAT Middle Level Math : Quadrilaterals

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #54 : Plane Geometry

Cube

 

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

Possible Answers:

Correct answer:

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 #21 : Quadrilaterals

Cube

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

 

Possible Answers:

Correct answer:

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 #4 : How To Find The Area Of A Square

Cube

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

Possible Answers:

Correct answer:

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 #5 : Geometry

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?

Possible Answers:

Correct answer:

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 #6 : How To Find The Area Of A Square

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.

Possible Answers:

Correct answer:

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 #7 : How To Find The Area Of A Square

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

Possible Answers:

Correct answer:

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 #1 : 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?

Possible Answers:

Correct answer:

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 #63 : Plane Geometry

Square

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.

Possible Answers:

The correct answer is not given among the other choices.

Correct answer:

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.

Possible Answers:

Correct answer:

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 #291 : Ssat Middle Level Quantitative (Math)

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 ?

Possible Answers:

Correct answer:

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 .

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