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

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

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Example Questions

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

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

Possible Answers:

Correct answer:

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 #2 : How To Find The 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 .

Possible Answers:

Correct answer:

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 #1 : How To Find The 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 .

Possible Answers:

Correct answer:

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 #4 : How To Find The 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 .

Possible Answers:

Correct answer:

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 #2 : How To Find The 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 .

Possible Answers:

Correct answer:

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 #3 : How To Find The Area Of A Parallelogram

Which of the following shapes is NOT a quadrilateral? 

Possible Answers:

Rhombus

Triangle

Square

Rectangle 

Kite

Correct answer:

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 #4 : How To Find The Area Of A Parallelogram

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

Possible Answers:

Their angle measurments

The sum of their angles 

The number of sides they each have 

Their side lengths 

Their color 

Correct answer:

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 #5 : How To Find The Area Of A Parallelogram

What two shapes can a square be classified as? 

Possible Answers:

Rectangle and Triangle 

Rectangle and Rhombas 

Trapezoid and Triangle 

Rhombus and Triangle 

Trapezoid and Rhombus 

Correct answer:

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 #6 : How To Find The Area Of A Parallelogram

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

Possible Answers:

The length of the sides

The color

The volume

The area

The number of sides

Correct answer:

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 #7 : How To Find The Area Of A Parallelogram

Which two shapes have to have  right angles? 

Possible Answers:

Square and Rhombus

Square and Parallelogram

Rectangle and Rhombus

Square and Rectangle 

Rectangle and Parallelogram

Correct answer:

Square and Rectangle 

Explanation:

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

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