ISEE Lower Level Math : Quadrilaterals

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

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Example Questions

Example Question #211 : Geometry

Find the perimeter of a square with a length of 7cm.

Possible Answers:

\(\displaystyle 28\text{cm}\)

\(\displaystyle 42\text{cm}\)

\(\displaystyle 21\text{cm}\)

\(\displaystyle 49\text{cm}\)

\(\displaystyle 56\text{cm}\)

Correct answer:

\(\displaystyle 28\text{cm}\)

Explanation:

To find the perimeter of a square, we will use the following formula:

\(\displaystyle P = a+b+c+d\)

where a, b, c, and d are the lengths of the sides of the square.

 

Now, we know the length of the square is 7cm.  Because it is a square, all sides are equal.  Therefore, all sides are 7cm.  So, we get

\(\displaystyle P = 7\text{cm} + 7\text{cm} + 7\text{cm} + 7\text{cm}\)

\(\displaystyle P = 28\text{cm}\)

Example Question #221 : Geometry

Use the square to answer the question.

Square_perimeter

What is the perimeter of the square?

Possible Answers:

\(\displaystyle 28ft\)

\(\displaystyle 35ft\)

\(\displaystyle 18ft\)

\(\displaystyle 14ft\)

\(\displaystyle 22ft\)

Correct answer:

\(\displaystyle 28ft\)

Explanation:

To find the perimeter of a square, add all the sides together:

\(\displaystyle 7\textup{ ft}+7\textup{ ft}+7\textup{ ft}+7\textup{ ft}=28\textup{ ft}\)

Example Question #72 : Squares

If the perimeter of a square is 18 cm, what must the area of this square be?

Possible Answers:

81cm2

20.25cm2

18cm2

16cm2

25cm2

Correct answer:

20.25cm2

Explanation:

Remember that a square has four sides, each side with equal lengths. If a square has a perimeter of 18 cm, that means that each side has a length of

18 ÷ 4 =

4.5 cm.

The formula for the area of a square is length x width or length squared (length x length), since each side of a square has the same length.

So,

4.5 x 4.5 =

20.25cm2

 

Example Question #73 : Squares

What is the area of a square that has a side with a length of 9 cm?

Possible Answers:

18

81

63

36

Correct answer:

81

Explanation:

The area of a square can be found using the same equation as the area of a rectangle - length times width.

\(\displaystyle A=l\times w\)

However, in the case of a square, all of the sides are of equal length. Therefore, the area of a square can be found using the equation:

\(\displaystyle A=l\times l\) or \(\displaystyle A=l^2\)

\(\displaystyle A=9^2=81\: cm^2\)

Example Question #3 : How To Find The Area Of A Square

What is the area of a square that has a side with a length of 10 in.?

Possible Answers:

\(\displaystyle 40\ in^{2}\)

\(\displaystyle 50\ in\)

\(\displaystyle 100\ in^{2}\)

\(\displaystyle 40\ in\)

\(\displaystyle 100\ in\)

Correct answer:

\(\displaystyle 100\ in^{2}\)

Explanation:

To calculate the area of a square, you need to multiply the length by the width. By definition, a square has 4 equal sides. So, by knowing the length of one side of the square, you know the length measurement and the width measurement.

Since the length of one side of this square is 10 in., you would multiply \(\displaystyle 10*10\) to get the answer.

\(\displaystyle 10*10=100\)

Because area is the number of squares that would be used to cover the inside the shape, it is given in units2. As a result, the answer is 100 in.2.

Example Question #4 : How To Find The Area Of A Square

The perimeter of a square is \(\displaystyle 32\; cm\) .  What is the area?

Possible Answers:

\(\displaystyle 48\; cm^{2}\)

\(\displaystyle 40\; cm^{2}\)

\(\displaystyle 96\; cm^{2}\)

\(\displaystyle 64\; cm^{2}\)

\(\displaystyle 16\; cm^{2}\)

Correct answer:

\(\displaystyle 64\; cm^{2}\)

Explanation:

The perimeter of a square is given by \(\displaystyle P=4s\).  Here \(\displaystyle 4s=32\), so divide by four to get \(\displaystyle s=8\).

The area of a square is given by \(\displaystyle A=s^{2}\). Substitute the side length obtained from the perimeter equation to get \(\displaystyle A=s^{2}=(8)^{2}=64 \; cm^{2}\).

Example Question #5 : How To Find The Area Of A Square

The perimeter of a square is \(\displaystyle 24\; cm\) .  What is the area?

Possible Answers:

\(\displaystyle 36\; cm^{2}\)

\(\displaystyle 28\; cm^{2}\)

\(\displaystyle 60\; cm^{2}\)

\(\displaystyle 20\; cm^{2}\)

\(\displaystyle 48\; cm^{2}\)

Correct answer:

\(\displaystyle 36\; cm^{2}\)

Explanation:

The perimeter of a square is given by \(\displaystyle P=4s\),  or \(\displaystyle 4s=24\). Divide by four to get \(\displaystyle s=6\).

The area of a square is given by \(\displaystyle A=s^{2}\). Substitute the side length obtained from the perimeter equation to get \(\displaystyle A=s^{2}=(6)^{2}=36 \; cm^{2}\).

Example Question #6 : How To Find The Area Of A Square

The perimeter of a square is \(\displaystyle 48\; in\).  What is the area?

Possible Answers:

\(\displaystyle 144\; in^{2}\)

\(\displaystyle 100\; in^{2}\)

\(\displaystyle 121\; in^{2}\)

\(\displaystyle 81\; in^{2}\)

\(\displaystyle 169\; in^{2}\)

Correct answer:

\(\displaystyle 144\; in^{2}\)

Explanation:

The perimeter of a square is given by \(\displaystyle P=4s\),  or \(\displaystyle 4s=48\). Divide by four to get \(\displaystyle s=12\).

The area of a square is given by \(\displaystyle A=s^{2}\). Substitute the value obtained from the perimeter equation to get \(\displaystyle A=s^{2}=(12)^{2}=144 \; in^{2}\).

 

Example Question #7 : How To Find The Area Of A Square

The perimeter of a square is \(\displaystyle 20\; in\) .  What is the area?

Possible Answers:

\(\displaystyle 24\; in^{2}\)

\(\displaystyle 16\; in^{2}\)

\(\displaystyle 12\; in^{2}\)

\(\displaystyle 9\; in^{2}\)

\(\displaystyle 25\; in^{2}\)

Correct answer:

\(\displaystyle 25\; in^{2}\)

Explanation:

The perimeter of a square is given by \(\displaystyle P=4s\),  or \(\displaystyle 4s=20\). Divide by four to get \(\displaystyle s=5\).

The area of a square is given by \(\displaystyle A=s^{2}\). Substitute the side length obtained from the perimeter equation to get \(\displaystyle A=s^{2}=(5)^{2}=25 \; in^{2}\).

Example Question #8 : How To Find The Area Of A Square

What is the area of a square with a side that measures \(\displaystyle 5\) feet?

Possible Answers:

\(\displaystyle 15\) square feet

\(\displaystyle 25\) square feet

\(\displaystyle 20\) square feet

\(\displaystyle 10\) square feet

Correct answer:

\(\displaystyle 25\) square feet

Explanation:

The area of a square can be found using the following formula:

\(\displaystyle A=s^{^{2}}\)

The side measures \(\displaystyle 5\) feet. 

\(\displaystyle 5^{2}=25\)

Therefore, the area of the square is \(\displaystyle 25\) square feet.

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