ISEE Lower Level Math : Rectangles

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

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Example Questions

Example Question #61 : 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:

\displaystyle 64\text{in}^2

\displaystyle 128\text{in}^2

\displaystyle 76\text{in}^2

\displaystyle 32\text{in}^2

\displaystyle 36\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 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 also know the width is half of the length.  Therefore, the width is 8in.

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

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

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

Example Question #71 : Plane Geometry

Find the area of the following rectangle:

Rectangle2

Possible Answers:

\displaystyle 27\text{in}^2

\displaystyle 55\text{in}^2

\displaystyle 22\text{in}^2

\displaystyle 32\text{in}^2

\displaystyle 16\text{in}^2

Correct answer:

\displaystyle 55\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, given the rectangle

Rectangle2

we can see the length is 11in and the width is 5in.  Knowing this, we can substitute into the formula.  We get

\displaystyle A = 11\text{in} \cdot 5\text{in}

\displaystyle A = 55\text{in}^2

Example Question #61 : How To Find The Area Of A Rectangle

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

Possible Answers:

\displaystyle 12\text{in}^2

\displaystyle 24\text{in}^2

\displaystyle 8\text{in}^2

\displaystyle 48\text{in}^2

\displaystyle 32\text{in}^2

Correct answer:

\displaystyle 32\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 4in.  We also know the length of the rectangle is two times the width.  Therefore, the length is 8in.  So, we get

\displaystyle A = 8\text{in} \cdot 4\text{in}

\displaystyle A = 32\text{in}^2

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

Dennis is building a fence around his field to keep his cattle from getting off the property. If Dennis’ field is \displaystyle \small 3 miles long and \displaystyle \small 2 miles wide, how much fence will Dennis need to surround all of his property?

Possible Answers:

\displaystyle 10\ mi

\displaystyle 6\ mi

\displaystyle 5\ mi

\displaystyle 12\ mi

\displaystyle 7\ mi

Correct answer:

\displaystyle 10\ mi

Explanation:

In order to determine how much fence Dennis will need, we must find the perimeter of his property, which can be found using the formula \displaystyle \small \small 2W+ 2L. When we plug \displaystyle \small 2\ mi in the \displaystyle \small W and \displaystyle \small 3\ mi in for \displaystyle \small L, we find that Dennis needs \displaystyle \small 10\ mi of fence to surround his property.

\displaystyle \small 2(2\ mi) + 2(3\ mi) = 10\ mi

 

 

 

 

 

 

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

Rectangle

Give the perimeter of the rectangle in the above diagram.

Possible Answers:

\displaystyle 116\textrm{ in}

\displaystyle 198\textrm{ in}

\displaystyle 99\textrm{ in}

\displaystyle 29\textrm{ in}

\displaystyle 58\textrm{ in}

Correct answer:

\displaystyle 58\textrm{ in}

Explanation:

Add the length and the height, then multiply the sum by two:

\displaystyle (11 + 18) \times 2 = 29 \times 2 = 58

The rectangle has a perimeter of 58 inches.

Example Question #72 : Plane Geometry

Rectangle

Give the perimeter of the above rectangle in feet.

Possible Answers:

\displaystyle 7 \frac{1}{2} \textrm{ ft}

\displaystyle 7 5\textrm{ ft}

\displaystyle 37 \frac{1}{2} \textrm{ ft}

\displaystyle 8\textrm{ ft}

\displaystyle 3 \frac{3}{4} \textrm{ ft}

Correct answer:

\displaystyle 7 \frac{1}{2} \textrm{ ft}

Explanation:

Use the following formula, substituting \displaystyle L = 30, W = 15 :

\displaystyle A = 2 (L + W)

\displaystyle A = 2 (30 + 15) = 2 \times 45 = 90 \textrm{ in}

Now, divide this by 12 to convert inches to feet.

\displaystyle \frac{90}{12} = 7 \textrm{ R }6

6 inches make half of a foot, so this means the perimeter is \displaystyle 7 \frac{1}{2} feet.

Example Question #91 : Geometry

What is the perimeter of a rectangle that has a length of \displaystyle \small 7 inches and a width of \displaystyle \small 4 inches? \displaystyle \small \left ( P=2l+2w\right )

Possible Answers:

\displaystyle \small 11

\displaystyle \small 22

\displaystyle \small 26

\displaystyle \small 28

Correct answer:

\displaystyle \small 22

Explanation:

The perimeter of a shape is the sum of all its sides. To find the perimeter of a rectangle, one can use the formula listed above, \displaystyle \small \left ( P= 2l+2w\right ), since a rectangle has opposite sides of equal length.

The length of the rectangle is \displaystyle \small 7:

\displaystyle \small 2\times7=14

The width of the rectangle is \displaystyle \small 4:

\displaystyle \small 4\times2=8.

\displaystyle \small 14+8=22

Therefore, the perimeter is \displaystyle \small 22.  

Example Question #92 : Geometry

What is the perimeter of a rectangle with length equal to 5 and width equal to 3?

Possible Answers:

16

8

15

30

Correct answer:

16

Explanation:

\displaystyle P=2(l+w)=2(5+3)=2(8)=16

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

What is the perimeter of a rectangle with a width of \displaystyle 5 and a length of \displaystyle 8?

Possible Answers:

\displaystyle 30

\displaystyle 26

\displaystyle 13

\displaystyle 40

Correct answer:

\displaystyle 26

Explanation:

The perimeter of a rectangle is equal to the sum of all its sides. The formula for finding the perimeter of a rectangle is \displaystyle P= 2(l+w)

The length of the rectangle is eight, and the width is five; \displaystyle 8+5=13.

\displaystyle 13\times2=26

Therefore, the perimeter of the rectangle is \displaystyle 26.

Example Question #2 : How To Find The Perimeter Of A Rectangle

Mr. Barker is building a rectangular fence. His yard has an area of \displaystyle 24 feet, and the one side of the fence he's already built is \displaystyle 6 feet long. 

What will the perimeter of his fence be when he is finished building it?

Possible Answers:

\displaystyle 36\ feet

\displaystyle 18\ feet

\displaystyle 24\ feet

\displaystyle 14\ feet

\displaystyle 20\ feet

Correct answer:

\displaystyle 20\ feet

Explanation:

The perimeter is calculated by adding up all the sides of the rectangle—in this case,

\displaystyle 6+6+4+4=20

So the perimeter is \displaystyle 20 feet.

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