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ISEE Middle Level Math : Rectangles

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Example Question #19 : How To Find The Area Of A Rectangle

Which of the following is equal to the area of a rectangle with length feet and width $1 \frac{1}{2}$ feet?

Possible Answers:

$576 \textrm{ in}^{2}$

$324\textrm{ in}^{2}$

$432 \textrm{ in}^{2}$

$648 \textrm{ in}^{2}$

Correct answer:

$648 \textrm{ in}^{2}$

Explanation:

Multiply each dimension by 12 to convert from feet to inches:

$3 \times 12 = 36 \textrm{ in}$

$1 \frac{1}{2} \times 12 = 18 \textrm{ in}$

Now multiply this length and width to get the area:

$36 \times 18 = 648 \textrm{ in}^{2}$

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Example Question #20 : How To Find The Area Of A Rectangle

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its surface area in square feet.

Possible Answers:

$13\frac{1}{4} \textrm{ ft}^{2}$

$15\frac{3}{4} \textrm{ ft}^{2}$

$16 \textrm{ ft}^{2}$

$32 \textrm{ ft}^{2}$

$14\frac{3}{4} \textrm{ ft}^{2}$

Correct answer:

$14\frac{3}{4} \textrm{ ft}^{2}$

Explanation:

Divide each dimension in inches by 12 to convert from inches to feet:

$L = 24 \div 12 = 2$ feet

$W = 18 \div 12 = 1 \frac{1}{2} = \frac{3}{2}$ feet

$H = 15 \div 12 = 1 \frac{1}{4} = \frac{5}{4}$ feet

Now, substitute in the surface area formula:

A = 2LW + 2WH + 2LH

$A = 2\cdot 2 \cdot \frac{3}{2} + 2 \cdot \frac{3}{2}\cdot \frac{5}{4} + 2\cdot 2 \cdot \frac{5}{4}$

$A =6 + \frac{15}{4} + 5$

$A =6 + 3 \frac{3}{4} + 5$

$A =14\frac{3}{4}ft^{2}$

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Example Question #101 : Plane Geometry

The area of a rectangle with a length of and a width of is $84\ in^2$ . Find .

Possible Answers:

1.21

1.11

1.31

1.41

1.51

Correct answer:

1.41

Explanation:

The area of a rectangle is the product of length and width:

$7x\times 6x=84\Rightarrow 42x^2=84\Rightarrow x^2=2\Rightarrow x=\sqrt{2}\approx 1.41$

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Example Question #1201 : Concepts

Give the area of a rectangle with a length of 3.8 ft and a width of $2.4\ ft$ .

Possible Answers:

$130\ in^2$

$1313.28\ in^2$

$1300\ in^2$

$1413.28\ in^2$

$131.28\ in^2$

Correct answer:

$1313.28\ in^2$

Explanation:

We know that:

$Area=a\times b$

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$Area=3.8\ ft \times 2.4\ ft=(3.8\times 12\ in)\times (2.4\times 12\ in)=1313.28\ in^2$

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Example Question #103 : Plane Geometry

A rectangular table has a length of $2.2\ m$ and a width of $1.5\ m$ . Give the area of the table.

Possible Answers:

$3300\ cm^2$

$330\ cm^2$

$33000\ cm^2$

$30000\ cm^2$

$3000\ cm^2$

Correct answer:

$33000\ cm^2$

Explanation:

We know that:

$Area=a\times b$

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$Area=2.2\ m \times 1.5\ m=(2.2\times 100\ cm)\times (1.5\times 100\ cm)=33000\ cm^2$

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Example Question #104 : Plane Geometry

The length of a rectangle is three times longer than its width. If the width of the rectangle is meters, give the area of the rectangle.

Possible Answers:

$30\ m^2$

$24\ m^2$

$27\ m^2$

$33\ m^2$

$21\ m^2$

Correct answer:

$27\ m^2$

Explanation:

The length of the rectangle would be: $3\times 3=9\ m$

We know that:

$Area=a\times b$

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$Area=9\times 3=27\ m^2$

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Example Question #105 : Plane Geometry

Which of the following is the area of a rectangle with a width of 4 feet and a length that is twice the width?

Possible Answers:

$32\ \text{ft}^2$

$64\ \text{ft}^2$

$36\ \text{ft}^2$

$34\ \text{ft}^2$

$16\ \text{ft}^2$

Correct answer:

$32\ \text{ft}^2$

Explanation:

The area of a rectangle is found by multiplying the width by the length.

$A=w\times l$

We know that the width is 4 feet and the the length must be twice the width. Multiply the width by 2 to find the length.

$l=2\times w$

$l=2\times4=8$

Multiply the length and width to find the area.

$4\times8=32$

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Example Question #11 : How To Find The Area Of A Rectangle

Jeff decided to build a play area for his guinea pigs. The play area would be an enclosure 6 feet long, 2 feet wide, and 2 feet tall. In cubic feet, how big is the play area?

Possible Answers:

$16\ ft^{3}$

$12\ ft^{3}$

$24\ ft^{3}$

$18\ ft^{3}$

Correct answer:

$24\ ft^{3}$

Explanation:

The cubic feet of an area is found by multiping the length times the width times the height. Given that the length is six feet, the width is two feet, and that the height is two feet, the total cubic area would be found using this equation:

$length\cdot width \cdot heighth$

Here is the equation with the appropriate numbers plugged in:

$6\cdot 2\cdot 2 = 24$

Therefore, 24 cubic feet is the correct answer.

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Example Question #1 : Area Of A Rectangle Or Square

Jessica's blanket is 12 square feet. Lisa has a blanket that is half the size of Jessica's blanket. Which of the following are possible dimensions of Lisa's blanket?

Possible Answers:

$3\ ft\times2\ ft$

$2\ ft\times2\ ft$

$3\ ft\times3\ ft$

$1\ ft\times12\ ft$

Correct answer:

$3\ ft\times2\ ft$

Explanation:

The area of a rectangle if found by multiplying the length times the width. Here, we know that Lisa's blanket is half the area of Jessica's blanket. Since Jessica's blanket is 12 square feet, that means that Lisa's blanket must be 6 square feet.

The only length and width values that give us 6 square feet when multiplied by one another are 3 feet by 2 feet. This is therefore the correct answer.

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Example Question #171 : Geometry

Rectangles

Note: Figure NOT drawn to scale.

What percent of the above figure is red?

Possible Answers:

The correct answer is not given among the other choices.

$90 \%$

$66 \frac{2}{3} \%$

$87 \frac{1}{2} \%$

$75 \%$

Correct answer:

The correct answer is not given among the other choices.

Explanation:

The large rectangle has length 80 and width 40, and, consequently, area

$80 \times 40 = 3,200$ .

The white region is a rectangle with length 30 and width 20, and, consequently, area

$30 \times 20 = 600$ .

The red region, therefore, has area 3,200 - 600 = 2,600 .

The red region is

$\frac{2,600}{3,200} \times 100 = 81 \frac{1}{4} \%$

of the large rectangle.

This is not one of the choices.

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ISEE Middle Level Math : Rectangles

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #19 : How To Find The Area Of A Rectangle

Example Question #20 : How To Find The Area Of A Rectangle

Example Question #101 : Plane Geometry

Example Question #1201 : Concepts

Example Question #103 : Plane Geometry

Example Question #104 : Plane Geometry

Example Question #105 : Plane Geometry

Example Question #11 : How To Find The Area Of A Rectangle

Example Question #1 : Area Of A Rectangle Or Square

Example Question #171 : Geometry

All ISEE Middle Level Math Resources

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