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

## Example Questions

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### Example Question #1 : 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 #51 : 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 .      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 #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 .      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 #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 .      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 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

Which of the following shapes is NOT a quadrilateral?

Rectangle

Triangle

Square

Kite

Rhombus

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?

The number of sides they each have

Their angle measurments

Their side lengths

The sum of their angles

Their color

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 two shapes can a square be classified as?

Trapezoid and Rhombus

Rectangle and Triangle

Rectangle and Rhombas

Rhombus and Triangle

Trapezoid and Triangle

Rectangle and Rhombas

Explanation:

A square can also be a rectangle and a rhombus because a rectangle has to have at least sets of equal side lengths and a rhombus has to have equal side lengths, like a square, and at least sets of equal angles.

### Example Question #3 : 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 length of the sides

The area

The volume

The color

The number of sides

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 #1 : How To Find The Area Of A Parallelogram

Which two shapes have to have right angles?

Square and Parallelogram

Rectangle and Parallelogram

Rectangle and Rhombus

Square and Rectangle

Square and Rhombus

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