SSAT Upper Level Math : Geometry

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

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Example Questions

Example Question #582 : Plane Geometry

Which of the shapes is NOT a quadrilateral? 

Possible Answers:

Rectangle 

Square

Rhombus

Hexagon

Trapezoid

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 #96 : Areas And Perimeters Of Polygons

Which of the following shapes is NOT a parallelogram? 

Possible Answers:

Rectangle

Kite

Square

Rhombus

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 #11 : How To Find The Area Of A Parallelogram

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

Possible Answers:

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 

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 #4 : Shape Properties

Which shape is NOT a quadrilateral?

Possible Answers:

Kite

Rhombus

Rectangle 

Trapezoid

Circle

Correct answer:

Circle

Explanation:

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

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

What other shape can a parallelogram be classified as? 

 

Possible Answers:

Rectangle 

Rhombus

Square

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 #831 : Geometry

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 #13 : How To Find The Area Of A Parallelogram

What two shapes can a square be classified as? 

Possible Answers:

Rectangle and Triangle 

Trapezoid and Rhombus 

Rhombus and Triangle 

Trapezoid and Triangle 

Rectangle and Rhombus 

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 #1 : 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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