SSAT Middle Level Math : Geometry

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

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Example Questions

Example Question #1 : How To Find The Perimeter Of A Rectangle

Rectangle

Give the perimeter of the rectangle in the above diagram.

Possible Answers:

Correct answer:

Explanation:

The perimeter of a rectangle can be calculated by multiplying two by the sum of the length and width of the rectangle.

The perimeter of the rectangle is  inches.

Example Question #111 : Geometry

Rectangle_1

Figure NOT drawn to scale.

Give the perimeter of the green polygon in the above figure.

Possible Answers:

The perimeter cannot be determined from the information given.

 

Correct answer:

Explanation:

Since opposite sides of a rectangle have the same measure, the missing sidelengths can be calculated as in the diagram below:

Rectangle_2

The sidelengths of the green polygon can now be added to find the perimeter:

Example Question #1 : How To Find The Perimeter Of A Rectangle

The width of a rectangle is one-third of its length. If the width is given as  what is the perimeter of the rectangle in terms of ?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a rectangle is the sum of its sides.

The sum of the widths is  and since the width is one-third of the length, each length is . Since there are  lengths we get a total of . Widths + lengths = 

Example Question #31 : Quadrilaterals

You are given equilateral triangle  and Rectangle 

with .

What is the perimeter of Rectangle  ?

Possible Answers:

Correct answer:

Explanation:

 is equilateral, so .

Also, since opposite sides of a rectangle are congruent, 

 and 

The perimeter of Rectangle  is 

Example Question #111 : Geometry

A hectare is a unit of area equal to 10,000 square meters.

A 150-hectare plot of land is rectangular and is 1.2 kilometers in width. Give the perimeter of this land.

Possible Answers:

Correct answer:

Explanation:

150 hectares is equal to  square meters.

The width of this land is 1.2 kilometers, or  meters. Divide the area by the width to get:

 meters

The perimeter of the land is 

 meters, or  kilometers.

Example Question #1 : How To Find The Perimeter Of A Rectangle

The length of a rectangle is two times as long as the width. The width is equal to  inches. What is the perimeter of the rectangle?

Possible Answers:

 

 

 

 

 

Correct answer:

 

 

 

 

 

Explanation:

Example Question #2 : How To Find The Perimeter Of The Rectangle

How many meters of fence are needed to enclose a rectangular field that has a length of 1000 meters and a width of 100 meters?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a rectangle is simply the sum of the four sides:

Example Question #11 : How To Find The Perimeter Of A Rectangle

The perimeter of a rectangle with a length of  and a width of is . Find .

 

Possible Answers:

Correct answer:

Explanation:

We know that:

 

 

where:

 

 

So we can write:

 

Example Question #301 : Ssat Middle Level Quantitative (Math)

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the perimeter of the red polygon.

Possible Answers:

The perimeter cannot be determined from the information given.

Correct answer:

Explanation:

Since opposite sides of a rectangle have the same measure, the missing sidelengths can be calculated as in the diagram below:

Rectangles

The sidelengths of the red polygon can now be added to find the perimeter:

Example Question #111 : Geometry

The width of a rectangle is , the length is , and the perimeter is 72. What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Start with the equation for the perimeter of a rectangle:

We know the perimeter is 72, the length is , and the width is . Plug these values into our equation.

Multiply and combine like terms.

Divide by 18 to isolate the variable.

Simplify the fraction by removing the common factor.

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