### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #53 : Geometry

A parallelogram has the base length of and the altitude of . Give the area of the parallelogram.

**Possible Answers:**

**Correct answer:**

The area of a parallelogram is given by:

Where is the base length and is the corresponding altitude. So we can write:

### Example Question #54 : Geometry

A parallelogram has a base length of which is 3 times longer than its corresponding altitude. The area of the parallelogram is 12 square inches. Give the .

**Possible Answers:**

**Correct answer:**

Base length is so the corresponding altitude is .

The area of a parallelogram is given by:

Where:

is the length of any base

is the corresponding altitude

So we can write:

### Example Question #55 : Geometry

The length of the shorter diagonal of a rhombus is 40% that of the longer diagonal. The area of the rhombus is . Give the length of the longer diagonal in terms of .

**Possible Answers:**

**Correct answer:**

Let be the length of the longer diagonal. Then the shorter diagonal has length 40% of this. Since 40% is equal to , 40% of is equal to .

The area of a rhombus is half the product of the lengths of its diagonals, so we can set up, and solve for , in the equation:

### Example Question #56 : Geometry

The length of the shorter diagonal of a rhombus is two-thirds that of the longer diagonal. The area of the rhombus is square yards. Give the length of the longer diagonal, in inches, in terms of .

**Possible Answers:**

**Correct answer:**

Let be the length of the longer diagonal in *yards*. Then the shorter diagonal has length two-thirds of this, or .

The area of a rhombus is half the product of the lengths of its diagonals, so we can set up the following equation and solve for :

To convert yards to inches, multiply by 36:

### Example Question #57 : Geometry

The longer diagonal of a rhombus is 20% longer than the shorter diagonal; the rhombus has area . Give the length of the shorter diagonal in terms of .

**Possible Answers:**

**Correct answer:**

Let be the length of the shorter diagonal. If the longer diagonal is 20% longer, then it measures 120% of the length of the shorter diagonal; this is

of , or .

The area of a rhombus is half the product of the lengths of its diagonals, so we can set up an equation and solve for :

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

Which of the following shapes is NOT a quadrilateral?

**Possible Answers:**

Rectangle

Square

Kite

Rhombus

Triangle

**Correct answer:**

Triangle

A quadrilateral is any two-dimensional shape with sides. The only shape listed that does not have sides is a triangle.

### Example Question #2 : How To Find The Area Of A Parallelogram

What is the main difference between a square and a rectangle?

**Possible Answers:**

The number of sides they each have

Their angle measurments

Their side lengths

Their color

The sum of their angles

**Correct answer:**

Their side lengths

The only difference between a rectangle and a square is their side lengths. A square has to have equal side lengths, but the opposite side lengths of a rectangle only have to be equal.

### Example Question #3 : How To Find The Area Of A Parallelogram

What is the main difference between a triangle and a rectangle?

**Possible Answers:**

The volume

The length of the sides

The area

The color

The number of sides

**Correct answer:**

The number of sides

Out of the choices given, the only characteristic used to describe shapes is the number of sides. A triangle has sides and a rectangle has sides.

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

Which two shapes have to have right angles?

**Possible Answers:**

Square and Rectangle

Rectangle and Rhombus

Square and Rhombus

Square and Parallelogram

Rectangle and Parallelogram

**Correct answer:**

Square and Rectangle

By definition, the only two quadrilaterals that have to have right angles, are the square and the rectangle.

### Example Question #2 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

Which of the shapes is NOT a quadrilateral?

**Possible Answers:**

Trapezoid

Rhombus

Rectangle

Hexagon

Square

**Correct answer:**

Hexagon

A quadrilateral is a sided shape. The only shape listed that does not have sides is a hexagon, which has sides.

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