ISEE Middle Level Math : Geometry

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

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Example Questions

Example Question #1963 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Find the area of a square with a base of length 8 inches.

Possible Answers:

\(\displaystyle 32\text{in}^2\)

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

\(\displaystyle 64\text{in}^2\)

\(\displaystyle 32\text{in}\)

\(\displaystyle 64\text{in}\)

Correct answer:

\(\displaystyle 64\text{in}^2\)

Explanation:

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

\(\displaystyle \text{area of square} = l \cdot w\)

where l is the length and w is the width of the square.

 

Now, we know the base has a length of 8 inches.  Because it is a square, we know that all sides are equal.  Therefore, all sides have a length of 8 inches.  This means the width is also 8 inches.  Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{area of square} = 8\text{in} \cdot 8\text{in}\)

\(\displaystyle \text{area of square} = 64\text{in}^2\)

Example Question #43 : Squares

Find the area of a square with a base of 12 inches.

Possible Answers:

\(\displaystyle 48\text{in}^2\)

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

\(\displaystyle 48\text{in}\)

\(\displaystyle \text{There is not enough information to solve the problem.}\)

\(\displaystyle 144\text{in}\)

Correct answer:

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

Explanation:

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

\(\displaystyle \text{area of square} = l \cdot w\)

where l is the length and w is the width of the square.

 

Now, we know the base of the square is 12in.  Because it is a square, we know that all sides are equal.  Which means all sides are 12in.  Therefore, the width is also 12in.  Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{area of square} = 12\text{in} \cdot 12\text{in}\)

\(\displaystyle \text{area of square} = 144\text{in}^2\)

Example Question #1964 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Find the area of a square with a width of 5 feet.

Possible Answers:

\(\displaystyle 15\text{ft}^2\)

\(\displaystyle \text{There is not enough information to solve the problem.}\)

\(\displaystyle 10\text{ft}^2\)

\(\displaystyle 20\text{ft}^2\)

\(\displaystyle 25\text{ft}^2\)

Correct answer:

\(\displaystyle 25\text{ft}^2\)

Explanation:

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

\(\displaystyle \text{area of square} = l \cdot w\)

where l is the length and w is the width of the rectangle.

 

Now, we know the width is 5 feet.  Because it is a square, all sides are equal.  This means the length is also 5 feet.

Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{area of square} = 5\text{ft} \cdot 5\text{ft}\)

\(\displaystyle \text{area of square} = 25\text{ft}^2\)

Example Question #44 : Squares

Find the area of a square with a width of 12cm.

Possible Answers:

\(\displaystyle 24\text{cm}^2\)

\(\displaystyle 144\text{cm}^2\)

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

\(\displaystyle 121\text{cm}^2\)

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

Correct answer:

\(\displaystyle 144\text{cm}^2\)

Explanation:

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

\(\displaystyle \text{area of square} = l \cdot w\)

where l is the length and w is the width of the square.

 

Now, we know the width of the square is 12cm.  Because it is a square, all sides are equal.  Therefore, the length is also 12cm.

Knowing this, we will substitute into the formula.  We get

\(\displaystyle \text{area of square} = 12\text{cm} \cdot 12\text{cm}\)

\(\displaystyle \text{area of square} = 144\text{cm}^2\)

Example Question #48 : Quadrilaterals

Use the following image to answer the question:

Square3

Find the area of the square.

Possible Answers:

\(\displaystyle 24\text{cm}^2\)

\(\displaystyle \text{There is not enough information to solve the problem.}\)

\(\displaystyle 32\text{cm}^2\)

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

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

Correct answer:

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

Explanation:

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

\(\displaystyle \text{area of square} = l \cdot w\)

where is the length and w is the width of the square.

 

Now, let's look at the given square.

Square3

We can see the width is 8cm.  Because it is a square, we know that all sides are equal.  Therefore, the width is also 8cm.

Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{area of square} = 8\text{cm} \cdot 8\text{cm}\)

\(\displaystyle \text{area of square} = 64\text{cm}^2\)

Example Question #41 : Squares

Find the area of a square with a length of 11in.

Possible Answers:

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

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

\(\displaystyle \text{There is not enough information to solve the problem.}\)

\(\displaystyle 22\text{in}^2\)

\(\displaystyle 44\text{in}^2\)

Correct answer:

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

Explanation:

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

\(\displaystyle \text{area of square} = l \cdot w\)

where l is the length and w is the width of the square.

 

Now, we know the length of the square is 11in.  Because it is a square, all sides are equal.  Therefore, the width is also 11in.

Knowing this, we will substitute into the formula.  We get

\(\displaystyle \text{area of square} = 11\text{in} \cdot 11\text{in}\)

\(\displaystyle \text{area of square} = 121\text{in}^2\)

Example Question #141 : Plane Geometry

Use the following square to answer the question:

Square2

Find the area.

Possible Answers:

\(\displaystyle 196\text{cm}^2\)

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

\(\displaystyle 56\text{cm}^2\)

\(\displaystyle 108\text{cm}^2\)

\(\displaystyle \text{There is not enough information to solve the problem.}\)

Correct answer:

\(\displaystyle 196\text{cm}^2\)

Explanation:

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

\(\displaystyle \text{area of square} = l \cdot w\)

where is the length and w is the width of the square.

 

Now, given the square

Square2

we can see the length is 14cm.  Because it is a square, all sides are equal.  Therefore, the width is also 14cm. 

Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{area of square} = 14\text{cm} \cdot 14\text{cm}\)

\(\displaystyle \text{area of square} = 196\text{cm}^2\)

 

Example Question #142 : Plane Geometry

Find the area of a square with a length of 8in.

Possible Answers:

\(\displaystyle 56\text{in}^2\)

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

\(\displaystyle 72\text{in}^2\)

\(\displaystyle 64\text{in}^2\)

\(\displaystyle 32\text{in}^2\)

Correct answer:

\(\displaystyle 64\text{in}^2\)

Explanation:

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

\(\displaystyle \text{area of square} = l \cdot w\)

where is the length and w is the width of the square.

 

So, we know the length of the square is 8in.  Because it is a square, all sides are equal.  Therefore, the width is also 8in. 

Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{area of square} = 8\text{in} \cdot 8\text{in}\)

\(\displaystyle \text{area of square} = 64\text{in}^2\)

Example Question #143 : Plane Geometry

Find the area of a square that has a width of 15in. 

Possible Answers:

\(\displaystyle 125\text{in}^2\)

\(\displaystyle 60\text{in}^2\)

\(\displaystyle 225\text{in}^2\)

\(\displaystyle 45\text{in}^2\)

\(\displaystyle 30\text{in}^2\)

Correct answer:

\(\displaystyle 225\text{in}^2\)

Explanation:

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

\(\displaystyle \text{area of square} = l \cdot w\)

where l is the length and w is the width of the square.

 

Now, we know the width of the square is 15in.  Because it is a square, all sides are equal.  Therefore, the length is also 15in.

Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{area of square} = 15\text{in} \cdot 15\text{in}\)

\(\displaystyle \text{area of square} = 225\text{in}^2\)

Example Question #144 : Plane Geometry

Find the area of a square with a base of 18cm.

Possible Answers:

\(\displaystyle 72\text{cm}^2\)

\(\displaystyle 324\text{cm}^2\)

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

\(\displaystyle 124\text{cm}^2\)

\(\displaystyle 248\text{cm}^2\)

Correct answer:

\(\displaystyle 324\text{cm}^2\)

Explanation:

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

\(\displaystyle \text{area of square} = l \cdot w\)

where l is the length and w is the width of the square.

 

Now, we know the base of the square is 18cm.  Because it is a square, all sides are equal.  Therefore, the length is also 18cm.

Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{area of square} = 18\text{cm} \cdot 18\text{cm}\)

\(\displaystyle \text{area of square} = 324\text{cm}^2\)

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