Squares

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ISEE Lower Level Quantitative Reasoning › Squares

Questions 1 - 10
1

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

\dpi{100} 4\ inches

\dpi{100} 2\ inches

\dpi{100} 8\ inches

\dpi{100} 16\ 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.

2

The perimeter of a triangle is 14 inches. One side is 4 inches long. Another side is 5 inches long. How long is the 3rd side?

\dpi{100} 4\ inches

Explanation

Add up all of the sides of a triangle to get the perimeter. Here, 2 of the sides add up to give you 9 inches. The third side must equal the difference between 14 inches and 9 inches.

3

What is the perimeter of the rectangle below?

Screen shot 2015 09 29 at 8.31.53 am

Explanation

The formula for perimeter of a rectangle is

To solve for the perimeter we can plug our known values into the equation.

4

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?

9 centimeters

81 centimeters

8 centimeters

20 centimeters

7 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.

5

Daria found the perimeter of the below trapezoid to be 29 inches.

Screenshot_2015-03-29_at_3.03.48_pm

What is the length of the missing side?

Explanation

To find the perimeter of a trapezoid, add up the lengths of its four sides. In the given trapezoid,

To find the missing side, combine like terms and solve for :

The missing side of the trapezoid is long.

6

What is the perimeter of the equilateral triangle below?

Screen shot 2015 11 09 at 8.59.58 am

Explanation

An equilateral triangle means that all of the side lengths are the same. To find the perimeter, we can take the one known side length and multiply by (since there are sides) or we can add the side length to itself times.

7

What is the perimeter of the triangle below?

Screen shot 2015 11 09 at 8.17.56 am

Explanation

To find the perimeter, we add all of the side lengths together.

8

One side of a square is centimeters long. What is the area of the square?

Explanation

The formula for finding the area of a square is , or, because this is a square, .

area = centimeters centimeters, or

9

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

What is the area of the rectangle made by 2 of these triangles aligned along the hypotenuse?

Explanation

If one combines the 2 identical triangles, their base and height become the length and width of the rectangle.

Area of a rectangle is:

In this case

10

Michaela drew th square below.

Screenshot_2015-03-25_at_3.13.25_pm

What is the area of the square?

144 square centimeters

48 square centimeters

12 square centimeters

100 square centimeters

112 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.

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