ISEE Middle Level Math : Rectangles

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

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Example Questions

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:

Correct answer:

Explanation:

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

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

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 a quarter of the length. 

Possible Answers:

Correct answer:

Explanation:

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

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.

 

Example Question #53 : 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:

Correct answer:

Explanation:

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

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

Example Question #54 : 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:

Correct answer:

Explanation:

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

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

Example Question #55 : 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:

Correct answer:

Explanation:

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

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

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:

Correct answer:

Explanation:

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

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

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

Find the area of a rectangle with the base of 12 and a height of 7.

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is:

Substitute the known lengths.

The answer is:  

Example Question #58 : How To Find The Area Of A Rectangle

Find the area of the following figure: 

L shape

Possible Answers:

Correct answer:

Explanation:

Construct an additional segment as shown below.

L shape

Note that the figure can be divided into two rectangles. Also note that, since opposite sides of a rectangle are of the same length, we can fill in some sidelengths, as noted above.

The two rectangles each have areas that are the product of their lengths and widths:

and 

Add these areas: , the area of the shape.

Area is written in square units; thus, 

Example Question #7 : How To Find The Perimeter Of A Rectangle

You are given equilateral triangle  and Rectangle 

with .

What is the perimeter of Rectangle  ?

Possible Answers:

Correct answer:

Explanation:

 is equilateral, so .

Also, since opposite sides of a rectangle are congruent, 

 and 

The perimeter of Rectangle  is 

Example Question #1 : How To Find The Perimeter Of A Rectangle

A hectare is a unit of area equal to 10,000 square meters.

A 150-hectare plot of land is rectangular and is 1.2 kilometers in width. Give the perimeter of this land.

Possible Answers:

Correct answer:

Explanation:

150 hectares is equal to  square meters.

The width of this land is 1.2 kilometers, or  meters. Divide the area by the width to get:

 meters

The perimeter of the land is 

 meters, or  kilometers.

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