SSAT Middle Level Math : Geometry

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

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Example Questions

Example Question #22 : How To Find The Area Of A Rectangle

What is the value of  if the angles of a quadrilateral are equal to  degrees,  degrees,  degrees, and

Possible Answers:

Correct answer:

Explanation:

Given that there are 360 degrees in a quadrilateral, 

Example Question #81 : Quadrilaterals

If the length of a rectangle is 7.5 feet and the width is 2 feet, what is the value of  if the area is ?

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is calculated by multiplying the length by the width. Here, the length is 7.5 and the width is 2, so the area will be 15. 

Given that the area is also equal to , the value of  will be 3, given that 3 times 5 is 15. 

Example Question #161 : Geometry

If a cereal box has a volume of 40 cubic inches, a width of 2 inches, and a height of 5 inches, what is its length? 

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a rectangular solid is .

Use the provided information from the question in the above formula and solve for the length.

Therefore, the length of the box is 4 inches. In answering this question, it is important to look at the units before selecting an answer. It is easy to be tricked into thinking that because the total answer is in cubic inches that it may be necessary to have square inches, but when multiplying three values, each with inches as their units, the units of the product will be cubic inches. 

Example Question #2 : How To Find The Volume Of A Figure

Swimming_pool

One cubic meter is equal to one thousand liters.

The above depicts a rectangular swimming pool for an apartment. The pool is  meters deep everywhere. How many liters of water does the pool hold?

Possible Answers:

Correct answer:

Explanation:

The pool can be seen as a rectangular prism with dimensions  meters by  meters by  meters; its volume in cubic meters is the product of these dimensions, which is 

 cubic meter.

One cubic meter is equal to one thousand liters, so multiply:

 liters of water.

Example Question #1231 : Concepts

Which of the following is equal to the area of a rectangle with length  meters and width  meters?

Possible Answers:

Correct answer:

Explanation:

Multiply each dimension by  to convert meters to centimeters:

Multiply these dimensions to get the area of the rectangle in square centimeters:

Example Question #81 : Quadrilaterals

Swimming_pool

The above depicts a rectangular swimming pool for an apartment. The pool is five feet deep everywhere.

An apartment manager wants to paint the four sides and the bottom of the swimming pool. One one-gallon can of the paint he wants to use covers  square feet. How many cans of the paint will the manager need to buy?

Possible Answers:

Correct answer:

Explanation:

The bottom of the swimming pool has area 

 square feet.

There are two sides whose area is 

 square feet,

and two sides whose area is 

 square feet.

Add the areas:

 square feet.

One one-gallon can of paint covers 350 square feet, so divide:

Seven full gallons and part of another are required, so eight is the correct answer.

Example Question #161 : Geometry

You are putting in a new carpet in your living room.  The dimensions of the the room are .  What is the square footage of carpet needed for the room?

Possible Answers:

Correct answer:

Explanation:

To find the area of a rectangle, you must multiply the two different side lengths.  For this room the answer would be  because .

Example Question #81 : Quadrilaterals

Rectangles 1

Refer to the above figures. The square at left has area 160. Give the area of the rectangle at right.

Possible Answers:

Correct answer:

Explanation:

The area of the square, whose sides have length , is the square of this sidelength, which is . The area of the rectangle is the product of the lengths of its sides; this is 

The square and the rectangle have the same area, so the correct response is 160.

Example Question #61 : Rectangles

Figures 2

Figure NOT drawn to scale.

Figure 1 and Figure 2 have the same area. The shaded portion of Figure 1 has area 64. What is the area of the shaded portion of Figure 2?

Possible Answers:

Correct answer:

Explanation:

Figure 1 is a rectangle divided into 24 squares of equal size; 3 of the squares are shaded, which means that  of Figure 1 is shaded.

Figure 2 is a circle  divided into 8 sectors of equal size; 1 is shaded, which means that  of Figure 2 is shaded.

Since the two figures are of the same area, the two shaded portions, each of which have an area that is the same fraction of this common area, must themselves have the same area. Since the shaded portion of Figure 1 has area 64, so does the shaded portion of Figure 2.

Example Question #1 : Parallelograms

Parallelogram

Note: Figure NOT drawn to scale

In the above diagram, 

Give the area of the parallelogram.

Possible Answers:

Correct answer:

Explanation:

The area of a parallelogram is its base multiplied by its height - represented by  and  here:

Note that the value of  is irrelevant.

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