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ISEE Upper Level Math : Plane Geometry

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All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #1 : Rectangles

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the area of your book cover?

Possible Answers:

96in

96in^2

40in^2

108in^2

Correct answer:

96in^2

Explanation:

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the area of your book cover?

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

$A_{rectangle}=l*w$

Plug in our knowns and solve:

A=8in*12in=96in^2

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

Find the area of a rectangle with a width of 5in and a length that is three times the width.

Possible Answers:

$15\text{in}^2$

$125\text{in}^2$

$50\text{in}^2$

$75\text{in}^2$

$25\text{in}^2$

Correct answer:

$75\text{in}^2$

Explanation:

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

$\text{area of rectangle} = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, we know the width of the rectangle is 5in. We also know the length is three times the width. Therefore, the length is 15in.

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

$\text{area of rectangle} = 15\text{in} \cdot 5\text{in}$

$\text{area of rectangle} = 75\text{in}^2$

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

Find the area of a rectangle with a width of 7cm and a length that is four times the width.

Possible Answers:

$148\text{cm}^2$

$22\text{cm}^2$

$56\text{cm}^2$

$196\text{cm}^2$

$28\text{cm}^2$

Correct answer:

$196\text{cm}^2$

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 width of the rectangle is 7cm. We also know the length is four times the width. Therefore, the length is 28cm.

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

$A = 28\text{cm} \cdot 7\text{cm}$

$A = 196\text{cm}^2$

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

Find the area of a rectangle with a width of 8cm and a length that is four times the width.

Possible Answers:

$96\text{cm}^2$

$256\text{cm}^2$

$128\text{cm}^2$

$80\text{cm}^2$

$32\text{cm}^2$

Correct answer:

$256\text{cm}^2$

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 width of the rectangle is 8cm. We also know the length of the rectangle is four times the width. Therefore, the length of the rectangle is 32cm.

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

$A = 32\text{cm} \cdot 8\text{cm}$

$A = 256\text{cm}^2$

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Example Question #2 : Rectangles

You are designing a poster to put on the front of your refrigerator. If the refrigerator door is 2 feet wide by 4.5 feet tall, what is the area of the largest poster you could fit on the door?

Possible Answers:

13 ft^2

20 ft^2

9 ft^2

15 ft^2

Correct answer:

9 ft^2

Explanation:

You are designing a poster to put on the front of your refrigerator. If the refrigerator door is 2 feet wide by 4.5 feet tall, what is the area of the largest poster you could fit on the door?

We need to find the area of a shape. Given the context of a refrigerator door and a poster, we can assume that the poster will be a rectangle. To find the area of a rectangle, we need to multiply length and width.

A=l*w=2ft*4.5ft=9ft^2

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Example Question #9 : How To Find The Area Of A Rectangle

A rectangle has a width of 9cm and a length that is three times the width. Find the area.

Possible Answers:

$324\text{cm}^2$

$81\text{cm}^2$

$27\text{cm}^2$

$243\text{cm}^2$

$216\text{cm}^2$

Correct answer:

$243\text{cm}^2$

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 width of the rectangle is 9cm. We also know the length of the rectangle is three times the width. Therefore, the length is 27cm. So, we can substitute.

$A = 27\text{cm} \cdot 9\text{cm}$

$A = 243\text{cm}^2$

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Example Question #10 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 12in and a width that is a third of the length.

Possible Answers:

$72\text{in}^2$

$56\text{in}^2$

$36\text{in}^2$

$24\text{in}^2$

$48\text{in}^2$

Correct answer:

$48\text{in}^2$

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 12in. We also know the width of the rectangle is a third of the length. Therefore, the width is 4in.

So, we get

$A = 12\text{in} \cdot 4\text{in}$

$A = 48\text{in}^2$

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

A >0 . Which is the greater quantity?

(a) The perimeter of the square on the coordinate plane with vertices (0,0), (A,0 ), (0,A), (A,A)

(b) The perimeter of the rectangle on the coordinate plane with vertices (0,0), (A+2,0 ), (0,A-2), (A+2,A-2)

Possible Answers:

(a) and (b) are equal.

It is impossible to tell from the information given.

(b) is greater.

(a) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

(a) The square has sidelength A - 0 = A , and therefore has perimeter .

(b) The rectangle has width A + 2 - 0 = A +2 and height A - 2 - 0 = A - 2 , so therefore has perimeter

$\left ( A + 2 \right ) + \left ( A - 2 \right ) + \left ( A + 2 \right ) + \left ( A - 2\right ) = A + A + A + A + 2- 2 + 2 - 2 = 4A$ .

The perimeters are the same.

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

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the perimeter of your book cover?

Possible Answers:

80 in^2

40 in^2

40 in

42 in

Correct answer:

40 in

Explanation:

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the perimeter of your book cover?

Perimeter is the distance around the outside of a shape.

Perimeter of a rectangle can be found via the following:

$P_{rectangle}=2l+2w$

Plug in our length and width to find our answer:

P=2(12in)+2(8in)=24in+16in=40in

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

Your aunt and uncle live on a rectangular plot of land out in the countryside. The width of their plot is $\frac{3}{4}$ of a kilometer long. The length is twice the width. What is the total length of the perimeter of the plot of land?

Possible Answers:

3.6 km

2.25 km

4.5 km

6 km

Correct answer:

4.5 km

Explanation:

Begin by finding both the width and length.

We are told that the width is $\frac{3}{4}$ of a kilometer

Further, we are told that the length is twice the width. Write this as an equation and solve:

$l=2w=2\frac{3}{4}=\frac{6}{4}=1\frac{1}{2}$

Now, find the perimeter via the following:

$P=2l+2w\rightarrow 2(\frac{3}{4}km)+ 2(\frac{3}{2}km)=1\frac{1}{2}km+3km=4.5km$

So, our perimeter is 4.5 km

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ISEE Upper Level Math : Plane Geometry

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : Rectangles

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

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

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

Example Question #2 : Rectangles

Example Question #9 : How To Find The Area Of A Rectangle

Example Question #10 : How To Find The Area Of A Rectangle

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

All ISEE Upper Level Math Resources

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