ISEE Lower Level Quantitative : Geometry

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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Example Questions

Example Question #3 : Squares

A square has an area of .  What is the length of one side?

Possible Answers:

\dpi{100} 16\ inches

\dpi{100} 2\ inches

\dpi{100} 4\ inches

\dpi{100} 8\ inches

Correct answer:

\dpi{100} 4\ inches

Explanation:

You can find the area of a square by multiplying two sides together.  All of the sides of a square are equal.  In this case, \dpi{100} 4\times 4=16, so the length of all of the sides of the square is 4 inches.

Example Question #5 : Squares

Michaela drew th square below.

Screenshot_2015-03-25_at_3.13.25_pm

What is the area of the square?

Possible Answers:

100 square centimeters

12 square centimeters

112 square centimeters

144 square centimeters

48 square centimeters

Correct answer:

144 square centimeters

Explanation:

The area of a square can be found by multiplying the length of a side times itself.  The side length of the above square is 12 cm. By finding 12 x 12, we find that the area of the square is 144 cm. squared.

Example Question #4 : Squares

James found the area of the square below to be 36 centimeters squared.

Screenshot_2015-03-25_at_3.13.12_pm

What is the length of one side of the square?

Possible Answers:

6 centimeters

9 centimeters

8 centimeters

36 centimeters

18 centimeters

Correct answer:

6 centimeters

Explanation:

The area of a square can be found by multiplying the length of a side by itself.  36 is equal to 6 times 6, therefore the length of one side is 6 centimeters. 

Example Question #5 : Squares

Daphne found the area of the square below to be 81 centimeters squared.

 

Screenshot_2015-03-25_at_3.13.12_pm

What is the length of one side of the square?

 

Possible Answers:

20 centimeters

9 centimeters

8 centimeters

7 centimeters

81 centimeters

Correct answer:

9 centimeters

Explanation:

The area of a square can be found by multiplying the length of a side by itself.  81 is equal to 9 times 9, therefore the length of one side is 9 centimeters. 

 

 

Example Question #2 : Squares

If the area of a square is , what is the length of each side?

Possible Answers:

Correct answer:

Explanation:

To find the area of a square, the length must be multiplied by the height.  Since a square has four equal sides, the length and width will have the same measurement. We must, therefore, find the square root of .  Since , is the square root of , which makes it the measurement for both the length and the width of the square.

Example Question #7 : Squares

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

Possible Answers:

Correct answer:

Explanation:

In order to find the perimeter of a rectangle, we must add the length of all the sides together. In this case, however, we must first determine the length, which can be found by multiplying by , because the length is four times the width, which had already been defined as .

Now we add together the four sides.

Example Question #6 : Squares

If the perimeter of a square is , what is the length of each side?

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a square, all the sides must be added together. Since a square has equal sides, the length of each side can be determined by dividing the perimeter () by .

Example Question #631 : Geometry

The perimeter of a square is . What is the length of one side?

Possible Answers:

Correct answer:

Explanation:

To find perimeter, add up all the sides. Since this is a square, all of the sides are going to be the same. So, you can divide  by  to find out what each side is. This gives an answer of

Example Question #632 : Geometry

One side of a square is  meters long. What is the perimeter of the square?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a shape is the distance around the shape. The area is the space within the shape. To find the perimeter of a shape, we simply add all the sides together. Since all of a square's sides are equal, and a square has four sides, use the formula:

 

Example Question #408 : Quadrilaterals

A right triangle has a base of  and a height of .

What is the perimeter of the rectangle made by combining 2 of these triangles along their hypotenuse?

Possible Answers:

Correct answer:

Explanation:

If the rectangle's length and width are 4 and 7, then perimeter, which is 

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