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ISEE Middle Level Math : Plane Geometry

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

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6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #51 : How To Find The Area Of A Rectangle

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

Possible Answers:

$20\text{in}^2$

$40\text{in}^2$

$4\text{in}^2$

$36\text{in}^2$

$64\text{in}^2$

Correct answer:

$64\text{in}^2$

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 know the width is a quarter of the length. So, we will divide the length by 4. Therefore, the width is 4in.

So, we can substitute.

$A = 16\text{in} \cdot 4\text{in}$

$A = 64\text{in}^2$

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Example Question #211 : Plane Geometry

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

Possible Answers:

$144\text{in}^2$

$64\text{in}^2$

$32\text{in}^2$

$96\text{in}^2$

$128\text{in}^2$

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 know the width is half the length. Therefore, the width is 8in. So, we can substitute. We get

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

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

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Example Question #54 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 20in and a width that is a quarter of the length.

Possible Answers:

$80\text{in}^2$

$50\text{in}^2$

$20\text{in}^2$

$100\text{in}^2$

$75\text{in}^2$

Correct answer:

$100\text{in}^2$

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 20in. We know the width is a quarter of the length. So, we will divide by 4. Therefore, the width is 5in. So, we can substitute. We get

$A = 20\text{in} \cdot 5\text{in}$

$A = 100\text{in}^2$

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Example Question #55 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 10in and a width that is half the length.

Possible Answers:

$30\text{in}^2$

$20\text{in}^2$

$25\text{in}^2$

$50\text{in}^2$

$45\text{in}^2$

Correct answer:

$50\text{in}^2$

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 10in. We also know the width of the rectangle is half the length. Therefore, the width is 5in. So, we get

$A = 10\text{in} \cdot 5\text{in}$

$A = 50\text{in}^2$

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Example Question #56 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 16cm and a width that is a quarter of the length.

Possible Answers:

$64\text{cm}^2$

$62\text{cm}^2$

$31\text{cm}^2$

$128\text{cm}^2$

$32\text{cm}^2$

Correct answer:

$64\text{cm}^2$

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 16cm. We also know the width of the rectangle is a quarter of the length. To find the width, we will divide 16 by 4. Therefore, the width the 4cm.

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

$A = 16\text{cm} \cdot 4\text{cm}$

$A = 64\text{cm}^2$

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Example Question #212 : Plane Geometry

Find the area of a rectangle with the base of 12 and a height of 7.

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is:

$A_{rectangle} = bh$

Substitute the known lengths.

$A_{rectangle} = (12)(7) = 84$

The answer is:

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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 #211 : Plane Geometry

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:

$5.4 \textrm{ km}$

$4.9 \textrm{ km}$

$2.45 \textrm{ km}$

$2.7 \textrm{ km}$

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 #4 : Rectangles

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:

$\small 32\ in$

$\small 40\ in$

$\small 24\ in$

$\small 16\ in$

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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ISEE Middle Level Math : Plane Geometry

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #51 : How To Find The Area Of A Rectangle

Example Question #211 : Plane Geometry

Example Question #54 : How To Find The Area Of A Rectangle

Example Question #55 : How To Find The Area Of A Rectangle

Example Question #56 : How To Find The Area Of A Rectangle

Example Question #212 : Plane Geometry

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

Example Question #212 : Plane Geometry

Example Question #211 : Plane Geometry

Example Question #4 : Rectangles

All ISEE Middle Level Math Resources

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