SSAT Upper Level Math : Geometry

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

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Example Questions

Example Question #5 : How To Find The Area Of A Parallelogram

Which of the shapes is NOT a quadrilateral? 

Possible Answers:

Square

Hexagon

Trapezoid

Rectangle 

Rhombus

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 #2 : 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

Square

Rhombus

Rectangle

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

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 side lengths 

There is no difference between them 

An isosceles trapezoid has to have equal base angles

A trapezoid has to have equal side lengths 

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 #8 : Shape Properties

Which shape is NOT a quadrilateral?

Possible Answers:

Circle

Kite

Rectangle 

Rhombus

Trapezoid

Correct answer:

Circle

Explanation:

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

Example Question #11 : How To Find The Area Of A Parallelogram

What other shape can a parallelogram be classified as? 

 

Possible Answers:

Square

Rectangle 

Rhombus

Quadrilateral 

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. 

Example Question #101 : Areas And Perimeters Of Polygons

Parallelogram

Figure NOT drawn to scale.

The above depicts Rhombus , which has perimeter 80. .

Give the area of  Rhombus .

Possible Answers:

Correct answer:

Explanation:

The area of any parallelogram is the product of the length of its base and that of a corresponding altitude. We can take  as a base and perpendicular  as an altitude.

All four sides of a rhombus have the same length, so we can find  by dividing the perimeter - the sum of the lengths of the four sides - by 4:

Now multiply the lengths of this base and the altitude to get the area:

Example Question #12 : How To Find The Area Of A Parallelogram

What two shapes can a square be classified as? 

Possible Answers:

Trapezoid and Triangle 

Rhombus and Triangle 

Rectangle and Rhombus 

Trapezoid and Rhombus 

Rectangle and Triangle 

Correct answer:

Rectangle and Rhombus 

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 #1 : How To Find The Perimeter Of A Parallelogram

The base length of a parallelogram is which is two times more than its side length. Give the perimeter of the parallelogram in terms of .

Possible Answers:

Correct answer:

Explanation:

The side length is half of the base length:

The perimeter of a parallelogram is:

Where:


  is the base length of the parallelogram and is the side length

 

Example Question #2 : How To Find The Perimeter Of A Parallelogram

The side length of a parallelogram is and the base length is three times more than side length. Give the perimeter of the parallelogram in terms of .

Possible Answers:

Correct answer:

Explanation:

The base length is three times more than the side length, so we have:

 

Base length

 

The perimeter of a parallelogram is:

Where:

is the base length of the parallelogram and  is the side length. So we get:

Example Question #3 : How To Find The Perimeter Of A Parallelogram

The base length of a parallelogram is 10 inches and the side length is 6 inches. Give the perimeter of the parallelogram.

Possible Answers:

Correct answer:

Explanation:

Like any polygon, the perimeter of a parallelogram is the total distance around the outside, which can be found by adding together the length of each side. In case of a parallelogram, each pair of opposite sides is the same length, so the perimeter is twice the base plus twice the side length. Or as a formula we can write:

 

Where:

is the base length of the parallelogram and is the side length. So we can write:

 

 

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