# SSAT Upper Level Math : How to find the area of a parallelogram

## Example Questions

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### Example Question #4 : Area Of A Parallelogram

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

Explanation:

The area of a parallelogram is given by:

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

### Example Question #1 : Area Of A Parallelogram

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 .

Explanation:

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 #6 : Area Of A Parallelogram

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 .

Explanation:

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 #7 : Area Of A Parallelogram

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 .

Explanation:

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 #8 : Area Of A Parallelogram

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 .

Explanation:

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 : Shape Properties

Which of the following shapes is NOT a quadrilateral?

Rhombus

Square

Triangle

Rectangle

Kite

Triangle

Explanation:

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

### Example Question #1 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

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

Their angle measurments

Their side lengths

The number of sides they each have

Their color

The sum of their angles

Their side lengths

Explanation:

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

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

The number of sides

The volume

The length of the sides

The area

The color

The number of sides

Explanation:

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 #2 : Shape Properties

Which two shapes have to have  right angles?

Rectangle and Rhombus

Square and Rectangle

Rectangle and Parallelogram

Square and Parallelogram

Square and Rhombus

Square and Rectangle

Explanation:

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

### Example Question #831 : Geometry

Which of the shapes is NOT a quadrilateral?

Square

Trapezoid

Rectangle

Hexagon

Rhombus