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ISEE Lower Level Math : Rectangles

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

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Example Questions

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Example Question #71 : Plane Geometry

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

Possible Answers:

$76\text{in}^2$

$32\text{in}^2$

$36\text{in}^2$

$64\text{in}^2$

$128\text{in}^2$

Correct answer:

$128\text{in}^2$

Explanation:

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

$A = l \cdot w$

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

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

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

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Example Question #71 : Quadrilaterals

Find the area of the following rectangle:

Rectangle2

Possible Answers:

$32\text{in}^2$

$27\text{in}^2$

$55\text{in}^2$

$22\text{in}^2$

$16\text{in}^2$

Correct answer:

$55\text{in}^2$

Explanation:

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

$A = l \cdot w$

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

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

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

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Example Question #76 : Plane Geometry

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

Possible Answers:

$32\text{in}^2$

$12\text{in}^2$

$24\text{in}^2$

$8\text{in}^2$

$48\text{in}^2$

Correct answer:

$32\text{in}^2$

Explanation:

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

$A = l \cdot w$

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

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

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

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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 $\small 3$ miles long and $\small 2$ miles wide, how much fence will Dennis need to surround all of his property?

Possible Answers:

$6\ mi$

$12\ mi$

$10\ mi$

$7\ mi$

$5\ mi$

Correct answer:

$10\ mi$

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 $\small \small 2W+ 2L$ . When we plug $\small 2\ mi$ in the $\small W$ and $\small 3\ mi$ in for $\small L$ , we find that Dennis needs $\small 10\ mi$ of fence to surround his property.

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

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

Rectangle

Give the perimeter of the rectangle in the above diagram.

Possible Answers:

$99\textrm{ in}$

$198\textrm{ in}$

$58\textrm{ in}$

$29\textrm{ in}$

$116\textrm{ in}$

Correct answer:

$58\textrm{ in}$

Explanation:

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

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

The rectangle has a perimeter of 58 inches.

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Example Question #3 : How To Find The Perimeter Of A Rectangle

Rectangle

Give the perimeter of the above rectangle in feet.

Possible Answers:

$7 5\textrm{ ft}$

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

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

$8\textrm{ ft}$

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

Correct answer:

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

Explanation:

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

A = 2 (L + W)

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

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

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

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

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Example Question #4 : How To Find The Perimeter Of A Rectangle

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

Possible Answers:

$\small 22$

$\small 26$

$\small 11$

$\small 28$

Correct answer:

$\small 22$

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, $\small \left ( P= 2l+2w\right )$ , since a rectangle has opposite sides of equal length.

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

$\small 2\times7=14$

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

$\small 4\times2=8$ .

$\small 14+8=22$

Therefore, the perimeter is $\small 22$ .

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Example Question #5 : How To Find The Perimeter Of A Rectangle

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

Possible Answers:

Correct answer:

Explanation:

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

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Example Question #6 : How To Find The Perimeter Of A Rectangle

What is the perimeter of a rectangle with a width of and a length of ?

Possible Answers:

Correct answer:

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 P= 2(l+w) .

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

$13\times2=26$

Therefore, the perimeter of the rectangle is .

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

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

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

Possible Answers:

$18\ feet$

$20\ feet$

$36\ feet$

$14\ feet$

$24\ feet$

Correct answer:

$20\ feet$

Explanation:

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

6+6+4+4=20

So the perimeter is feet.

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ISEE Lower Level Math : Rectangles

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #71 : Plane Geometry

Example Question #71 : Quadrilaterals

Example Question #76 : Plane Geometry

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

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

Example Question #3 : How To Find The Perimeter Of A Rectangle

Example Question #4 : How To Find The Perimeter Of A Rectangle

Example Question #5 : How To Find The Perimeter Of A Rectangle

Example Question #6 : How To Find The Perimeter Of A Rectangle

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

All ISEE Lower Level Math Resources

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