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ISEE Middle Level Math : Quadrilaterals

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Example Questions

Example Question #53 : How To Find The Area Of A Rectangle

Find the area of the following figure:

L shape

Possible Answers:

$850\textup{ units}^2$

$450\textup{ units}^2$

$300\textup{ units}^2$

$750\textup{ units}^2$

$800\textup{ units}^2$

Correct answer:

$750\textup{ units}^2$

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:

$10 \times 30 = 300$

and

$15 \times 30 = 450$

Add these areas: 300 + 450 = 750 , the area of the shape.

Area is written in square units; thus, $750\textup{ units}^2$

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Example Question #212 : Plane Geometry

You are given equilateral triangle $\Delta ABC$ and Rectangle ACDE

with AB = 25, CD = 40 .

What is the perimeter of Rectangle ACDE ?

Possible Answers:

160

115

130

180

Correct answer:

130

Explanation:

$\Delta ABC$ is equilateral, so AC = AB = 25 .

Also, since opposite sides of a rectangle are congruent,

DE = AC = 25 and AE = CD = 40

The perimeter of Rectangle ACDE is

AC + CD +DE + AE = 25 + 40 + 25 + 40 = 130

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Example Question #121 : Quadrilaterals

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:

$2.7 \textrm{ km}$

$2.45 \textrm{ km}$

$5.4 \textrm{ km}$

$4.9 \textrm{ km}$

Correct answer:

$4.9 \textrm{ km}$

Explanation:

150 hectares is equal to $150 \times 10,000 = 1,500,000$ square meters.

The width of this land is 1.2 kilometers, or $1.2 \times 1,000 =1,200$ meters. Divide the area by the width to get:

$1,500,000 \div 1,200 = 1,250$ meters

The perimeter of the land is

$2 \left ( 1,200 + 1,250\right ) = 4,900$ meters, or $4,900 \div 1,000 = 4.9$ kilometers.

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Example Question #122 : Quadrilaterals

The length of a rectangle is two times as long as the width. The width is equal to inches. What is the perimeter of the rectangle?

Possible Answers:

$\small 32\ in$

$\small 24\ in$

$\small 16\ in$

$\small 40\ in$

Correct answer:

$\small 24\ in$

Explanation:

l=2w=2(4)=8

P=l+w+l+w=2l+2w=2(8)+2(4)=16+8=24

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Example Question #62 : Rectangles

How many meters of fence are needed to enclose a rectangular field that has a length of 1000 meters and a width of 100 meters?

Possible Answers:

$10,000\ meters$

$100,000\ meters$

$2000\ meters$

$2200\ meters$

$1100\ meters$

Correct answer:

$2200\ meters$

Explanation:

The perimeter of a rectangle is simply the sum of the four sides:

$1000+1000+100+100=2200\; meters$

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Example Question #31 : Quadrilaterals

The perimeter of a rectangle with a length of 10x and a width of is $64\ in$ . Find .

Possible Answers:

Correct answer:

Explanation:

We know that:

Perimeter=2(a+b)

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$64=2(10x+6x)\Rightarrow 10x+6x=32\Rightarrow 16x=32\Rightarrow x=2$

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Example Question #63 : Rectangles

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the perimeter of the red polygon.

Possible Answers:

240

The perimeter cannot be determined from the information given.

340

120

140

Correct answer:

240

Explanation:

Since opposite sides of a rectangle have the same measure, the missing sidelengths can be calculated as in the diagram below:

Rectangles

The sidelengths of the red polygon can now be added to find the perimeter:

40 + 80 + 20 + 30 + 20 + 50 = 240

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Example Question #125 : Quadrilaterals

The width of a rectangle is , the length is , and the perimeter is 72. What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Start with the equation for the perimeter of a rectangle:

P=l+l+w+w=2l+2w

We know the perimeter is 72, the length is , and the width is . Plug these values into our equation.

72=2(6x)+2(3x)

Multiply and combine like terms.

72=12x+6x

72=18x

Divide by 18 to isolate the variable.

$\frac{72}{18}=x$

Simplify the fraction by removing the common factor.

$\frac{72}{18}=\frac{72\div18}{18\div18}=\frac{4}{1}=4$

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Example Question #126 : Quadrilaterals

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the ratio of the perimeter of the large rectangle to that of the smaller rectangle.

Possible Answers:

2:1

12:5

The correct answer is not given among the other choices.

16:7

8:3

Correct answer:

12:5

Explanation:

Opposite sides of a rectangle are congruent.

The large rectangle has perimeter

40 + 80 + 40 + 80 = 240 .

The smaller rectangle has perimeter

20 + 30 + 20 + 30 = 100 .

The ratio is

$\frac{240}{100} = \frac{240 \div 20 }{100\div 20 } = \frac{12}{5}$ ; that is, 12 to 5.

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Example Question #123 : Quadrilaterals

What is the perimeter of a rectangle with a width of 3 and a length of 10?

Possible Answers:

Correct answer:

Explanation:

The formula for the perimeter of a rectangle is $\dpi{100} Perimeter=2l+2w$ .

Plug in our given values to solve:

$\dpi{100} Perimeter = 2(20)+2(3)$

$\dpi{100} Perimeter = 20+6$

$\dpi{100} Perimeter = 26$

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ISEE Middle Level Math : Quadrilaterals

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #53 : How To Find The Area Of A Rectangle

Example Question #212 : Plane Geometry

Example Question #121 : Quadrilaterals

Example Question #122 : Quadrilaterals

Example Question #62 : Rectangles

Example Question #31 : Quadrilaterals

Example Question #63 : Rectangles

Example Question #125 : Quadrilaterals

Example Question #126 : Quadrilaterals

Example Question #123 : Quadrilaterals

All ISEE Middle Level Math Resources

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