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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #206 : Plane Geometry

Find the area of a rectangle with a width of 8in and a length that is two times the width.

Possible Answers:

$20\text{in}^2$ $\displaystyle 20\text{in}^2$

$114\text{in}^2$ $\displaystyle 114\text{in}^2$

$48\text{in}^2$ $\displaystyle 48\text{in}^2$

$16\text{in}^2$ $\displaystyle 16\text{in}^2$

$128\text{in}^2$ $\displaystyle 128\text{in}^2$

Correct answer:

$128\text{in}^2$ $\displaystyle 128\text{in}^2$

Explanation:

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

$\text{area of rectangle} = l \cdot w$ $\displaystyle \text{area of rectangle} = l \cdot w$

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

Now, we know the width of the rectangle is 8in. We also know the length is two times the width. Therefore, the length is 16in.

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

$\text{area of rectangle} = 16\text{in} \cdot 8\text{in}$ $\displaystyle \text{area of rectangle} = 16\text{in} \cdot 8\text{in}$

$\text{area of rectangle} = 128\text{in}^2$ $\displaystyle \text{area of rectangle} = 128\text{in}^2$

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Example Question #207 : Plane Geometry

Find the area of a rectangle with a length of 24in and a width that is a third of the length.

Possible Answers:

$192\text{in}^2$ $\displaystyle 192\text{in}^2$

$72\text{in}^2$ $\displaystyle 72\text{in}^2$

$212\text{in}^2$ $\displaystyle 212\text{in}^2$

$156\text{in}^2$ $\displaystyle 156\text{in}^2$

$96\text{in}^2$ $\displaystyle 96\text{in}^2$

Correct answer:

$192\text{in}^2$ $\displaystyle 192\text{in}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

Now, we know the length of the rectangle is 24in. We also know the width is a third of the length. Therefore, the width is 8in.

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

$A = 24\text{in} \cdot 8\text{in}$ $\displaystyle A = 24\text{in} \cdot 8\text{in}$

$A = 196\text{in}^2$ $\displaystyle A = 196\text{in}^2$

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Example Question #43 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a width of 6in and a length that is four times the width.

Possible Answers:

$96\text{in}^2$ $\displaystyle 96\text{in}^2$

$144\text{in}^2$ $\displaystyle 144\text{in}^2$

$121\text{in}^2$ $\displaystyle 121\text{in}^2$

$136\text{in}^2$ $\displaystyle 136\text{in}^2$

$48\text{in}^2$ $\displaystyle 48\text{in}^2$

Correct answer:

$144\text{in}^2$ $\displaystyle 144\text{in}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

Now, we know the width of the rectangle is 6in. We also know the length is four times the width. Therefore, the length is 24in.

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

$A = 24\text{in} \cdot 6\text{in}$ $\displaystyle A = 24\text{in} \cdot 6\text{in}$

$A = 144\text{in}^2$ $\displaystyle A = 144\text{in}^2$

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Example Question #44 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 21in and a width that is a third of the length.

Possible Answers:

$147\text{in}^2$ $\displaystyle 147\text{in}^2$

$49\text{in}^2$ $\displaystyle 49\text{in}^2$

$84\text{in}^2$ $\displaystyle 84\text{in}^2$

$63\text{in}^2$ $\displaystyle 63\text{in}^2$

$126\text{in}^2$ $\displaystyle 126\text{in}^2$

Correct answer:

$147\text{in}^2$ $\displaystyle 147\text{in}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

We know the length of the rectangle is 21in. We also know the width of the rectangle is a third of the length. Therefore, the width is 7in.

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

$A = 21\text{in} \cdot 7\text{in}$ $\displaystyle A = 21\text{in} \cdot 7\text{in}$

$A = 147\text{in}^2$ $\displaystyle A = 147\text{in}^2$

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Example Question #51 : How To Find The Area Of A Rectangle

Use the following rectangle to answer the question:

Rectangle1

Find the area.

Possible Answers:

$9\text{in}^2$ $\displaystyle 9\text{in}^2$

$18\text{in}^2$ $\displaystyle 18\text{in}^2$

$36\text{in}^2$ $\displaystyle 36\text{in}^2$

$24\text{in}^2$ $\displaystyle 24\text{in}^2$

$15\text{in}^2$ $\displaystyle 15\text{in}^2$

Correct answer:

$18\text{in}^2$ $\displaystyle 18\text{in}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

Now, given the rectangle

Rectangle1

we can see the length is 6in and the width is 3in. Knowing this, we can substitute into the formula. So, we get

$A = 6\text{in} \cdot 3\text{in}$ $\displaystyle A = 6\text{in} \cdot 3\text{in}$

$A = 18\text{in}^2$ $\displaystyle A = 18\text{in}^2$

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Example Question #51 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 16in and a width that is a quarter of the length.

Possible Answers:

$36\text{in}^2$ $\displaystyle 36\text{in}^2$

$40\text{in}^2$ $\displaystyle 40\text{in}^2$

$64\text{in}^2$ $\displaystyle 64\text{in}^2$

$4\text{in}^2$ $\displaystyle 4\text{in}^2$

$20\text{in}^2$ $\displaystyle 20\text{in}^2$

Correct answer:

$64\text{in}^2$ $\displaystyle 64\text{in}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

Now, we know the length of the rectangle is 16in.

We know the width is a quarter of the length. So, we will divide the length by 4. Therefore, the width is 4in.

So, we can substitute.

$A = 16\text{in} \cdot 4\text{in}$ $\displaystyle A = 16\text{in} \cdot 4\text{in}$

$A = 64\text{in}^2$ $\displaystyle A = 64\text{in}^2$

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Example Question #52 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 16in and a width that is half the length.

Possible Answers:

$64\text{in}^2$ $\displaystyle 64\text{in}^2$

$128\text{in}^2$ $\displaystyle 128\text{in}^2$

$32\text{in}^2$ $\displaystyle 32\text{in}^2$

$144\text{in}^2$ $\displaystyle 144\text{in}^2$

$96\text{in}^2$ $\displaystyle 96\text{in}^2$

Correct answer:

$128\text{in}^2$ $\displaystyle 128\text{in}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

Now, we know the length of the rectangle is 16in. We know the width is half the length. Therefore, the width is 8in. So, we can substitute. We get

$A = 16\text{in} \cdot 8\text{in}$ $\displaystyle A = 16\text{in} \cdot 8\text{in}$

$A =128\text{in}^2$ $\displaystyle A =128\text{in}^2$

Report an Error

Example Question #53 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 20in and a width that is a quarter of the length.

Possible Answers:

$75\text{in}^2$ $\displaystyle 75\text{in}^2$

$50\text{in}^2$ $\displaystyle 50\text{in}^2$

$20\text{in}^2$ $\displaystyle 20\text{in}^2$

$80\text{in}^2$ $\displaystyle 80\text{in}^2$

$100\text{in}^2$ $\displaystyle 100\text{in}^2$

Correct answer:

$100\text{in}^2$ $\displaystyle 100\text{in}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

Now, we know the length of the rectangle is 20in. We know the width is a quarter of the length. So, we will divide by 4. Therefore, the width is 5in. So, we can substitute. We get

$A = 20\text{in} \cdot 5\text{in}$ $\displaystyle A = 20\text{in} \cdot 5\text{in}$

$A = 100\text{in}^2$ $\displaystyle A = 100\text{in}^2$

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Example Question #54 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 10in and a width that is half the length.

Possible Answers:

$25\text{in}^2$ $\displaystyle 25\text{in}^2$

$20\text{in}^2$ $\displaystyle 20\text{in}^2$

$50\text{in}^2$ $\displaystyle 50\text{in}^2$

$30\text{in}^2$ $\displaystyle 30\text{in}^2$

$45\text{in}^2$ $\displaystyle 45\text{in}^2$

Correct answer:

$50\text{in}^2$ $\displaystyle 50\text{in}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

Now, we know the length of the rectangle is 10in. We also know the width of the rectangle is half the length. Therefore, the width is 5in. So, we get

$A = 10\text{in} \cdot 5\text{in}$ $\displaystyle A = 10\text{in} \cdot 5\text{in}$

$A = 50\text{in}^2$ $\displaystyle A = 50\text{in}^2$

Report an Error

Example Question #56 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 16cm and a width that is a quarter of the length.

Possible Answers:

$64\text{cm}^2$ $\displaystyle 64\text{cm}^2$

$62\text{cm}^2$ $\displaystyle 62\text{cm}^2$

$31\text{cm}^2$ $\displaystyle 31\text{cm}^2$

$128\text{cm}^2$ $\displaystyle 128\text{cm}^2$

$32\text{cm}^2$ $\displaystyle 32\text{cm}^2$

Correct answer:

$64\text{cm}^2$ $\displaystyle 64\text{cm}^2$

Explanation:

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

$A = l \cdot w$ $\displaystyle A = l \cdot w$

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

Now, we know the length of the rectangle is 16cm. We also know the width of the rectangle is a quarter of the length. To find the width, we will divide 16 by 4. Therefore, the width the 4cm.

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

$A = 16\text{cm} \cdot 4\text{cm}$ $\displaystyle A = 16\text{cm} \cdot 4\text{cm}$

$A = 64\text{cm}^2$ $\displaystyle A = 64\text{cm}^2$

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #206 : Plane Geometry

Example Question #207 : Plane Geometry

Example Question #43 : How To Find The Area Of A Rectangle

Example Question #44 : How To Find The Area Of A Rectangle

Example Question #51 : How To Find The Area Of A Rectangle

Example Question #51 : How To Find The Area Of A Rectangle

Example Question #52 : How To Find The Area Of A Rectangle

Example Question #53 : How To Find The Area Of A Rectangle

Example Question #54 : How To Find The Area Of A Rectangle

Example Question #56 : How To Find The Area Of A Rectangle

All ISEE Middle Level Math Resources

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