SSAT Upper Level Math : Areas and Perimeters of Polygons

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

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Example Questions

Example Question #2 : 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 #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? 

Possible Answers:

Rhombus

Triangle

Kite

Rectangle 

Square

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 #42 : Geometry

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

Possible Answers:

The number of sides they each have 

Their side lengths 

Their angle measurments

The sum of their angles 

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 #4 : 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?

Possible Answers:

The area

The color

The number of sides

The length of the sides

The volume

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

Which two shapes have to have  right angles? 

Possible Answers:

Rectangle and Rhombus

Rectangle and Parallelogram

Square and Rectangle 

Square and Rhombus

Square 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. 

Example Question #4 : 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

Hexagon

Rectangle 

Rhombus

Square

Correct answer:

Hexagon

Explanation:

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

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

Which of the following shapes is NOT a parallelogram? 

Possible Answers:

Kite

Rhombus

Rectangle

Square

Correct answer:

Kite

Explanation:

A rectangle, square, and rhombus can all be classified as a parallelogram because each shape has opposite side lengths that are equal. A kite does not. 

Example Question #6 : Shape Properties

What is the difference between a trapezoid and a isosceles trapezoid? 

Possible Answers:

A trapezoid has to have equal side lengths 

An isosceles trapezoid has to have equal base angles

An isosceles trapezoid has to have equal side lengths 

There is no difference between them 

A trapezoid has to have equal base angles

Correct answer:

An isosceles trapezoid has to have equal base angles

Explanation:

By definition, an isosceles trapezoid has to have  equal base angles, but a trapezoid does not have to have equal angles. 

Example Question #7 : Shape Properties

Which shape is NOT a quadrilateral?

Possible Answers:

Rhombus

Rectangle 

Circle

Trapezoid

Kite

Correct answer:

Circle

Explanation:

A quadrilateral has to have  sides, a circle does not have any sides. 

Example Question #61 : Geometry

What other shape can a parallelogram be classified as? 

 

Possible Answers:

Rectangle 

Rhombus

Triangle 

Square

Quadrilateral 

Correct answer:

Quadrilateral 

Explanation:

A parallelogram can not be classified as a square because a square has to have  equal sides, but a parallelogram can have two different side lengths, as long as the opposite side lengths are equal. 

A parallelogram can not be classified as a rectangle because a rectangle has to have  angles, and a parallelogram does not. 

A parallelogram can not be classified as a triangle because a parallelogram has to have  sides and a triangle only has  sides. 

A parallelogram can not be classified as a rhombus because a rhombus has to have  equal sides and a parallelogram does not. 

A parallelogram has four sides, and all shapes with four sides are quadrilaterals. 

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