ISEE Middle Level Math : How to find the area of a rectangle

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

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Example Questions

Example Question #193 : Geometry

Use the following image to answer the question:

Rectangle3

Find the area of the rectangle.

Possible Answers:

\(\displaystyle 63\text{in}^2\)

\(\displaystyle 54\text{in}^2\)

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

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

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

Correct answer:

\(\displaystyle 54\text{in}^2\)

Explanation:

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

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

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

 

Now, let's look at the rectangle.

Rectangle3

We can see the length is 9 inches, and the width is 6 inches. 

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

\(\displaystyle \text{area of rectangle} = 9\text{in} \cdot 6\text{in}\)

\(\displaystyle \text{area of rectangle} = 54\text{in}^2\)

Example Question #41 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a width of 4in and a length that is three times the width.

Possible Answers:

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

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

\(\displaystyle 14\text{in}^2\)

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

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

Correct answer:

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

Explanation:

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

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

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

 

Now, we know the width of the rectangle is 4in.  We also know the length of the rectangle is three times the width.  Therefore, the length is 12in. 

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

\(\displaystyle \text{area of rectangle} = 12\text{in} \cdot 4\text{in}\)

\(\displaystyle \text{area of rectangle} = 48\text{in}^2\)

Example Question #42 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a width of 9cm and a length that is two times the width.

Possible Answers:

\(\displaystyle 162\text{cm}^2\)

\(\displaystyle 128\text{cm}^2\)

\(\displaystyle 18\text{cm}^2\)

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

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

Correct answer:

\(\displaystyle 162\text{cm}^2\)

Explanation:

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

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

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

 

Now, we know the width of the rectangle is 9cm.  We also know the length of the rectangle is two times the width.  Therefore, the length is 18cm.

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

\(\displaystyle \text{area of rectangle} = 18\text{cm} \cdot 9\text{cm}\)

\(\displaystyle \text{area of rectangle} = 162\text{cm}^2\)

Example Question #201 : Geometry

Find the area of a rectangle with a width of 4in and a length that is three times the width.

Possible Answers:

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

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

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

\(\displaystyle 17\text{in}^2\)

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

Correct answer:

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

Explanation:

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

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

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

 

Now, we know the width of the rectangle is 4in.  We also know the length is three times the width.  Therefore, the length is 12in.  

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

\(\displaystyle \text{area of rectangle} = 12\text{in} \cdot 4\text{in}\)

\(\displaystyle \text{area of rectangle} = 48\text{in}^2\)

Example Question #204 : Plane Geometry

Find the area of a rectangle with a width of 3cm and a length that is three times the width.  

Possible Answers:

\(\displaystyle 9\text{cm}^2\)

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

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

\(\displaystyle 27\text{cm}^2\)

\(\displaystyle 12\text{cm}^2\)

Correct answer:

\(\displaystyle 27\text{cm}^2\)

Explanation:

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

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

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

 

So, we know the width of the rectangle is 3cm.  We also know the length is three times the width.  Therefore, the length is 9cm.  

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

\(\displaystyle \text{area of rectangle} = 9\text{cm} \cdot 3\text{cm}\)

\(\displaystyle \text{area of rectangle} = 27\text{cm}^2\)

Example Question #41 : Rectangles

Find the area of a rectangle with a length of 12cm and a width that is a quarter of the length.

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

 

Now, we know the length of the rectangle is 12cm.  We also know the width of the rectangle is a quarter of the length.  To find the width, we will divide 12 by 4.  Therefore, the width the 3cm.

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

\(\displaystyle \text{area of rectangle} = 12\text{cm} \cdot 3\text{cm}\)

\(\displaystyle \text{area of rectangle} = 36\text{cm}^2\)

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:

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

\(\displaystyle 114\text{in}^2\)

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

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

\(\displaystyle 128\text{in}^2\)

Correct answer:

\(\displaystyle 128\text{in}^2\)

Explanation:

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

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

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

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

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

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:

\(\displaystyle 192\text{in}^2\)

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

\(\displaystyle 212\text{in}^2\)

\(\displaystyle 156\text{in}^2\)

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

Correct answer:

\(\displaystyle 192\text{in}^2\)

Explanation:

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

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

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

 

\(\displaystyle A = 24\text{in} \cdot 8\text{in}\)

\(\displaystyle A = 196\text{in}^2\)

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:

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

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

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

\(\displaystyle 136\text{in}^2\)

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

Correct answer:

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

Explanation:

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

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

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

\(\displaystyle A = 24\text{in} \cdot 6\text{in}\)

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

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:

\(\displaystyle 147\text{in}^2\)

\(\displaystyle 49\text{in}^2\)

\(\displaystyle 84\text{in}^2\)

\(\displaystyle 63\text{in}^2\)

\(\displaystyle 126\text{in}^2\)

Correct answer:

\(\displaystyle 147\text{in}^2\)

Explanation:

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

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

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

\(\displaystyle A = 21\text{in} \cdot 7\text{in}\)

\(\displaystyle A = 147\text{in}^2\)

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