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ISEE Middle Level Math : Rectangles

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Example Questions

Example Question #21 : How To Find The Area Of A Rectangle

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the ratio of the area of the red region to that of the white region.

Possible Answers:

13:3 $\displaystyle 13:3$

The correct answer is not given among the other choices.

25:7 $\displaystyle 25:7$

3:1 $\displaystyle 3:1$

7:1 $\displaystyle 7:1$

Correct answer:

13:3 $\displaystyle 13:3$

Explanation:

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

$80 \times 40 = 3,200$ $\displaystyle 80 \times 40 = 3,200$.

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

$30 \times 20 = 600$ $\displaystyle 30 \times 20 = 600$.

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

The ratio of the area of the red region to that of the white region is

$\frac{2,600}{600} = \frac{2,800 \div 200}{600\div 200 }= \frac{13}{3}$ $\displaystyle \frac{2,600}{600} = \frac{2,800 \div 200}{600\div 200 }= \frac{13}{3}$

That is, 13 to 3.

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Example Question #21 : How To Find The Area Of A Rectangle

Swimming_pool

The above figure depicts the rectangular swimming pool at an apartment. The apartment manager needs to purchase a tarp that will cover this pool completely, but the store will only sell the material in multiples of one hundred square meters. How many square meters will the manager need to buy?

Possible Answers:

Insufficient information is given to answer the question.

$600\textrm{ m}^{2}$ $\displaystyle 600\textrm{ m}^{2}$

$500\textrm{ m}^{2}$ $\displaystyle 500\textrm{ m}^{2}$

$300\textrm{ m}^{2}$ $\displaystyle 300\textrm{ m}^{2}$

$400\textrm{ m}^{2}$ $\displaystyle 400\textrm{ m}^{2}$

Correct answer:

$400\textrm{ m}^{2}$ $\displaystyle 400\textrm{ m}^{2}$

Explanation:

The tarp needed to cover this pool must be, at minimum, the product of its length and width, or

$24 \times 15 = 360$ $\displaystyle 24 \times 15 = 360$ square meters.

The manager will need to buy a number of square yards of tarp equal to the next highest multiple of one hundred, which is 400 square meters.

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Example Question #71 : Quadrilaterals

The four angles of a square are labeled A, B, C, and D. What is the sum of A+B+C $\displaystyle A+B+C$?

Possible Answers:

300^o $\displaystyle 300^o$

180^o $\displaystyle 180^o$

90^o $\displaystyle 90^o$

270^o $\displaystyle 270^o$

More information is needed to solve

Correct answer:

270^o $\displaystyle 270^o$

Explanation:

In a square, each angle is 90 degrees.

$\displaystyle A=B=C=D=90^o$

We can plug in 90 for each variable and find the sum.

$\displaystyle A+B+C=90^o+90^o+90^o=270^o$

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Example Question #52 : Rectangles

Swimming_pool

The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere.

An apartment manager wants to paint the four sides and the bottom of the swimming pool. How many square feet will he need to paint?

Possible Answers:

$1,020 \textrm{ ft}^{2}$ $\displaystyle 1,020 \textrm{ ft}^{2}$

$2,770 \textrm{ ft}^{2}$ $\displaystyle 2,770 \textrm{ ft}^{2}$

$10,500 \textrm{ ft}^{2}$ $\displaystyle 10,500 \textrm{ ft}^{2}$

The correct answer is not given among the other responses.

$4,520 \textrm{ ft}^{2}$ $\displaystyle 4,520 \textrm{ ft}^{2}$

Correct answer:

$2,770 \textrm{ ft}^{2}$ $\displaystyle 2,770 \textrm{ ft}^{2}$

Explanation:

The bottom of the swimming pool has area

$50 \times 35 = 1,750$ $\displaystyle 50 \times 35 = 1,750$ square feet.

There are two sides whose area is

$50 \times 6 = 300$ $\displaystyle 50 \times 6 = 300$ square feet,

and two sides whose area is

$35 \times 6 = 210$ $\displaystyle 35 \times 6 = 210$ square feet.

Add the areas:

$\displaystyle 1,750 + 300 + 300 + 210 +210=2,770$ square feet.

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Example Question #53 : Rectangles

If the angles of a quadrilateral are equal to $\displaystyle b$, $\displaystyle 2b$, $\displaystyle 3b$, and $\displaystyle 3b$, what is the value of $\displaystyle b$?

Possible Answers:

$\displaystyle 50$

$\displaystyle 60$

$\displaystyle 70$

$\displaystyle 40$

Correct answer:

$\displaystyle 40$

Explanation:

Given that there are 360 degrees in a quadrilateral,

$\displaystyle b+2b+3b+3b=360$

9b=360 $\displaystyle 9b=360$

b=40 $\displaystyle b=40$

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Example Question #54 : Rectangles

What is the value of $\displaystyle w$ if the angles of a quadrilateral are equal to $\displaystyle 50$ degrees, 110 $\displaystyle 110$ degrees, $\displaystyle 80$ degrees, and $\displaystyle 2w$?

Possible Answers:

$\displaystyle 62$

$\displaystyle 65$

$\displaystyle 60$

$\displaystyle 74$

Correct answer:

$\displaystyle 60$

Explanation:

Given that there are 360 degrees in a quadrilateral,

$\displaystyle 50 + 110 +80 + 2w=360$

$\displaystyle 240+2w=360$

2w=120 $\displaystyle 2w=120$

w=60 $\displaystyle w=60$

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Example Question #161 : Geometry

If the length of a rectangle is 7.5 feet and the width is 2 feet, what is the value of $\displaystyle x$ if the area is $\displaystyle 5x$?

Possible Answers:

$\displaystyle 5$

$\displaystyle 3$

$\displaystyle 2$

$\displaystyle 15$

Correct answer:

$\displaystyle 3$

Explanation:

The area of a rectangle is calculated by multiplying the length by the width. Here, the length is 7.5 and the width is 2, so the area will be 15.

Given that the area is also equal to $\displaystyle 5x$, the value of $\displaystyle x$ will be 3, given that 3 times 5 is 15.

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Example Question #57 : Rectangles

Which of the following is equal to the area of a rectangle with length 4.3 $\displaystyle 4.3$ meters and width 3.5 $\displaystyle 3.5$ meters?

Possible Answers:

$155,000 \textrm{ cm}^{2}$ $\displaystyle 155,000 \textrm{ cm}^{2}$

$15,050 \textrm{ cm}^{2}$ $\displaystyle 15,050 \textrm{ cm}^{2}$

$150,500 \textrm{ cm}^{2}$ $\displaystyle 150,500 \textrm{ cm}^{2}$

$15,500 \textrm{ cm}^{2}$ $\displaystyle 15,500 \textrm{ cm}^{2}$

Correct answer:

$150,500 \textrm{ cm}^{2}$ $\displaystyle 150,500 \textrm{ cm}^{2}$

Explanation:

Multiply each dimension by 100 $\displaystyle 100$ to convert meters to centimeters:

$4.3 \times 100 = 430$ $\displaystyle 4.3 \times 100 = 430$

$3.5 \times 100 = 350$ $\displaystyle 3.5 \times 100 = 350$

Multiply these dimensions to get the area of the rectangle in square centimeters:

$430 \times 350 = 150,500\textrm{ cm}^{2}$ $\displaystyle 430 \times 350 = 150,500\textrm{ cm}^{2}$

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Example Question #21 : Rectangles

Find the area of a rectangle whose length is 6 and width is 5.

Possible Answers:

$\displaystyle 30$

$\displaystyle 5$

$\displaystyle 22$

$\displaystyle 15$

Correct answer:

$\displaystyle 30$

Explanation:

To solve, simply use the formula for the area of a rectangle.

In this particular case the length and width are given,

$\displaystyle l=6, w=5$.

Thus:

$\displaystyle area=l*w=6*5=30$

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Example Question #184 : Geometry

The area of a four-sided room that has dimensions of $10\times12$ $\displaystyle 10\times12$ will be the four wall lengths all added to together. True or False?

Possible Answers:

False

True

Correct answer:

False

Explanation:

The area of a rectangle is the length times the width. So to calculate it, you must multiple the two different lengths together. Adding the four wall lengths would get you the perimeter instead.

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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 #21 : How To Find The Area Of A Rectangle

Example Question #21 : How To Find The Area Of A Rectangle

Example Question #71 : Quadrilaterals

Example Question #52 : Rectangles

Example Question #53 : Rectangles

Example Question #54 : Rectangles

Example Question #161 : Geometry

Example Question #57 : Rectangles

Example Question #21 : Rectangles

Example Question #184 : Geometry

All ISEE Middle Level Math Resources

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