SSAT Middle Level Math : Plane Geometry

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

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Example Questions

Example Question #11 : Rectangles

Rectangle ABCD has an area of .  If the width of the rectangle is , what is the perimeter?

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is found by multiplying the length times the width.  The question tells you the width is  and the area is .  

Thus the length is 8. .

To find the perimeter you add up all of the sides.  

 

Example Question #5 : How To Find The Perimeter Of The Rectangle

If the perimeter of a rectangle is  inches and the width is  inches, what is the length?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a rectangle is represented by the following formula, in which W represents width and L represents length:

Given that the width is  inches and that the perimeter is  inches, the following applies:

Next, subtract  from each side.

Now, divide each side by .

This gives us

Example Question #42 : Quadrilaterals

A rectangle has an area of . The length of each side is a whole number. What is NOT a possible value for the rectangle's perimeter? 

Possible Answers:

Correct answer:

Explanation:

Since each side is a whole number, first find the whole number factors of . They are  and ,  and ,  and , and  and . These sidelengths correspond to perimeters of , , , and , respectively. Thus,  is answer. 

Example Question #43 : Quadrilaterals

Rectangle

Give the perimeter of the above rectangle in centimeters, using the conversion factor  centimeters per yard.

Possible Answers:

Correct answer:

Explanation:

The perimeter of the rectangle is  yards. To convert this to centimeters, multiply by the given conversion factor:

 centimeters.

Example Question #44 : Quadrilaterals

Find the perimeter of the rectangle shown below

Screen shot 2015 11 10 at 9.55.29 pm

Possible Answers:

Correct answer:

Explanation:

The perimeter of a rectangle, or any shape, is the distance around the outside. You add up the length of each side to find this number. The coordinates of the points are . You need to find the distance between each point. The short side is  units, and the longer side is  units. 

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

Steve's bedroom measures 20' by 18' by 8' high. He wants to paint the ceiling and all four walls using a paint that gets 360 square feet of coverage per gallon. A one-gallon can of the paint Steve wants costs $36.00; a one-quart can costs $13.00. What is the least amount of money that Steve can expect to spend on paint in order to paint his room?

Possible Answers:

Correct answer:

Explanation:

Two of the walls have area ; two have area ; the ceiling has area 

Therefore, the total area Steve wants to cover is 

Divide 968 by 360 to get the number of gallons Steve needs to paint his bedroom:

Since , Steve needs to purchase either two gallon cans and three quart cans, or three gallon cans. 

The first option will cost him ; the second option will cost him . The latter is the more economical option.

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

Rectangle

Give the area of the rectangle in the above diagram.

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is the product of its length and its height:

The rectangle has a perimeter of 80.64 square centimeters.

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

 

Rectangle

Give the area of the rectangle in the above diagram.

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is the product of its length and its width:

The area of the rectangle is 42 square inches.

Example Question #242 : Geometry

Prism

Give the surface area of the above box in square centimeters.

Possible Answers:

Correct answer:

Explanation:

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

 centimeters

 centimeters

Use the surface area formula, substituting :

 square centimeters

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

Thingy

Above is a figure that comprises a red square and a white rectangle. The ratio of the length of the white rectangle to the sidelength of the square is . What percent of the entire figure is red?

Possible Answers:

Correct answer:

Explanation:

To make this easier, we will assume that the rectangle has length 5 and the square has sidelength 3. Then the area of the entire figure is 

,

and the area of the square is 

The square, therefore, takes up

of the entire figure.

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