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 #4 : 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:

Kite

Triangle

Square

Rhombus

Rectangle 

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 #2 : 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?

Possible Answers:

Their angle measurments

Their side lengths 

The sum of their angles 

The number of sides they each have 

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 #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?

Possible Answers:

The area

The number of sides

The length of the sides

The color

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:

Square and Rhombus

Rectangle and Rhombus

Rectangle and Parallelogram

Square and Rectangle 

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 #1 : Shape Properties

Which of the shapes is NOT a quadrilateral? 

Possible Answers:

Trapezoid

Hexagon

Rhombus

Square

Rectangle 

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 #7 : 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:

Square

Rhombus

Rectangle

Kite

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 #2 : Shape Properties

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

Possible Answers:

A trapezoid has to have equal base angles

An isosceles trapezoid has to have equal base angles

An isosceles trapezoid has to have equal side lengths 

A trapezoid has to have equal side lengths 

There is no difference between them 

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 #2 : Shape Properties

Which shape is NOT a quadrilateral?

Possible Answers:

Rhombus

Trapezoid

Circle

Kite

Rectangle 

Correct answer:

Circle

Explanation:

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

Example Question #831 : Geometry

What other shape can a parallelogram be classified as? 

 

Possible Answers:

Quadrilateral 

Rectangle 

Rhombus

Square

Triangle 

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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