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ISEE Lower Level Math : Rectangles

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Example Questions

Example Question #11 : Plane Geometry

Screen_shot_2013-08-20_at_5.07.49_pm

What is the total surface area of the enclosed region?

Possible Answers:

126cm²

112cm²

114cm²

212cm²

168cm²

Correct answer:

114cm²

Explanation:

Screen_shot_2013-08-20_at_5.21.33_pm

First, we must find the missing lengths. Because we know that the length going horizontally across on the bottom is 6 cm and 8 cm, that must mean that the length going across at the top must also equal this sum.

So, the length of the top must equal

6 + 8 =

14.

We are given one value of the length on the top, 4. To find the missing horizontal length on the top, we must subtract 4 from 14.

14 – 4 = 10.

In order to find the other missing length, we must observe that the greatest vertical length of this figure is 12 cm. Because we are given 4 cm and 5 cm, we must subtract 4 and 5 from 12 to find the other missing length.

12 – 4 – 5 =

Now, let's divide this enclosed region in three separate rectangles.

The rectangle at the top has a length of 4 cm and width of 3 cm.

The middle rectangle has a length of

10 + 4 =

14 cm

and a width of 5 cm.

The bottom rectangle has a length of 8 cm and width of 4 cm.

If the formula for the area of a rectangle is length x width, we must now calculate the individual areas of each rectangle and add them up.

Area of top rectangle

4 x 3 = 12cm²

Area of middle rectangle

14 x 5 = 70cm²

Area of bottom rectangle

8 x 4 = 32cm²

12cm² + 32cm² + 70cm²=

114cm²

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Example Question #1 : Rectangles

Mr. Barker is building a rectangular fence. His yard has an area of 24 feet, and the one side of the fence he's already built is 6 feet long.

What is the length of the other side (the width) of the fence?

Possible Answers:

$8\ feet$

$7\ feet$

$2\ feet$

$12\ feet$

$4\ feet$

Correct answer:

$4\ feet$

Explanation:

The answer is 4 feet, because $area=width\times length$

and a rectangle must have 4 sides, with 2 sides of one length and 2 sides of another.

$6\times 4=24$ feet

making the other side 4 feet,

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Example Question #2 : Rectangles

If Bailey is making a quilt for a bed that measures feet wide and feet long, and she wants there to be an extra foot of quilt to hang over each side of the bed, how much material should she buy.

Possible Answers:

$48 ft^{2}$

$63 ft^{2}$

$82 ft^{2}$

$80 ft^{2 }$

$78 ft^{2}$

Correct answer:

$80 ft^{2 }$

Explanation:

In order to determine how much material Bailey needs, we must first find the area of space she needs to cover. Since Bailey would like the quilt to be an extra foot on each side, we must add feet to both the length and width.

Width 6ft +2ft = 8ft

Length 8ft +2ft = 10ft

Now we apply the formula for the area of a rectangle, which is $L\times W$ .

$10\cdot 8= 80 ft^{2}$

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Example Question #2 : How To Find The Area Of A Rectangle

Rectangle

Give the area of the rectangle in the above diagram.

Possible Answers:

$29 \textrm{ in}^2$

$198 \textrm{ in}^2$

$116\textrm{ in}^2$

$99 \textrm{ in}^2$

$58 \textrm{ in}^2$

Correct answer:

$198 \textrm{ in}^2$

Explanation:

Multiply the length by the width to get the area of the rectangle:

$18 \times 11 = 198$

The area of the rectangle is 198 square inches.

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Example Question #3 : Rectangles

Which could be the dimensions of a rectangle with the area $36\textup{ cm}^{2}$ ?

Possible Answers:

$18 \textup{ cm}\times 18 \textup{ cm}$

$4 \textup{ cm}\times 8 \textup{ cm}$

$3 \textup{ cm}\times 12 \textup{ cm}$

$2 \textup{ cm}\times 13 \textup{ cm}$

Correct answer:

$3 \textup{ cm}\times 12 \textup{ cm}$

Explanation:

To find the area, simply multiply the sides of the rectangle. The only sides which add up to are:

$3 \textup{ cm}\times 12 \textup{ cm}$

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

Rectangle

Give the area of the above rectangle in square centimeters.

Possible Answers:

$100,000 \textrm{ cm}^{2}$

$10,000 \textrm{ cm}^{2}$

$50,000 \textrm{ cm}^{2}$

$140,000 \textrm{ cm}^{2}$

$70,000 \textrm{ cm}^{2}$

Correct answer:

$100,000 \textrm{ cm}^{2}$

Explanation:

Since 1 meter = 100 centimeters, multiply each dimension by 100 to convert meters to centimeters. This makes the dimensions 200 centimeters by 500 centimeters.

Use the area formula, substituting L = 500, W = 200 :

A = LW

$A = 500 \times 200 = 100,000 \textrm{ cm}^{2}$

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Example Question #4 : Rectangles

Mr. Smith is planting a rectangular garden with a length of 5 ft and a width of 7 ft. What is the area of the garden?

Possible Answers:

24ft^2

28ft^2

35ft^2

20ft^2

Correct answer:

35ft^2

Explanation:

The area of a rectangle can be calculated by multiplying the length by the width.

$A=l\times w=5\: ft\times7\: ft=35\: ft^2$

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Example Question #8 : How To Find The Area Of A Rectangle

Sally's room measures 100 square feet. Which type of measurement is this?

Possible Answers:

Perimeter

Width

Volume

Area

Length

Correct answer:

Area

Explanation:

Area is measured in units squared, and volume is measured in units cubed. Width, length, and perimeter are all measured in regular units.

Therefore, 100 square feet is the area of the room.

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Example Question #5 : Rectangles

Robert needs to determine the area of his rectangular wall in order to buy the proper amount of paint at the store. When he measures his wall he determines that it is 12 feet high and 20 feet wide. If one can of paint covers 40 square feet of wall, how many cans of paint does Robert need?

Possible Answers:

$\dpi{100} 6$

$\dpi{100} 7$

$\dpi{100} 4$

$\dpi{100} 8$

Correct answer:

$\dpi{100} 6$

Explanation:

Find the area of the wall - $\dpi{100} 12\times 20=240$

Divide $\dpi{100} 240\div 40=6$

6 cans of paint.

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Example Question #4 : How To Find The Area Of A Rectangle

What is the area of a rectangle with a length of $\small 5$ feet and a width of $\small 25$ feet?

Possible Answers:

$\small 30$ square feet

$\small 125$ square feet

$\small 100$ square feet

250 square feet

$\small 60$ square feet

Correct answer:

$\small 125$ square feet

Explanation:

To find the area of a rectangle, multiply the length by the width.

$\small 5\times25=125$

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ISEE Lower Level Math : Rectangles

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #11 : Plane Geometry

Example Question #1 : Rectangles

Example Question #2 : Rectangles

Example Question #2 : How To Find The Area Of A Rectangle

Example Question #3 : Rectangles

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

Example Question #4 : Rectangles

Example Question #8 : How To Find The Area Of A Rectangle

Example Question #5 : Rectangles

Example Question #4 : How To Find The Area Of A Rectangle

All ISEE Lower Level Math Resources

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