Rectangles - ISEE Lower Level (grades 5-6) Mathematics Achievement

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Question

What is the total surface area of the enclosed region?

Answer

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 =

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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Question

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?

Answer

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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Question

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.

Answer

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

Length

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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Question

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?

Answer

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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Question

Give the area of the rectangle in the above diagram.

Answer

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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Question

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

Answer

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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Question

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?

Answer

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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Question

Give the area of the above rectangle in square centimeters.

Answer

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 :

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

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Question

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

Answer

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

$\small 5\times25=125$

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Question

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

Answer

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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Question

Joe has a rectangular poster that is 3 feet long and 2 feet wide. What is the area of the poster?

Answer

The area of a rectangle is found by multiping the length times the width. Given that the length is 3 feet, the width is 2 feet, the total cubic area would be found using this equation:

$\text{length}\times \text{width} = \text{area}$

Here is the equation with the appropriate numbers plugged in from the question:

$3\ \text{ft}\times2\ \text{ft}=6\ \text{ft}^2$

6 square feet, or $6\ \text{ft}^2$ is the correct answer.

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Question

Leslie has a blanket that is $14\ \text{ft}^2$ in area. Jen has a blanket that is half the size of Leslie's blanket. How big is Jen's blanket?

Answer

If Jen's blanket is half as big as Leslie's blanket, and Leslie's blanket is $14\ \text{ft}^2$ , then we need to divide by 2 to find the area of Jen's blanket.

$14\ \text{ft}^2\div2=7\ \text{ft}^2$

The area of Jen's blanket is $7\ \text{ft}^2$ .

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Question

If a rectangle has an area of 18, which of the following are possible dimensions of the length and width?

Answer

If the area of the rectangle is 18, that means that the length and the width, when multiplied together, should equal 18.

$A=l\times w=18$

The only numbers from the answer choices that would result in the product of 18 are 9 by 2, which is therefore the correct answer.

$l=9,\ w=2$

$9\times2=18$

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Question

What is the area (in square feet) of a rectangle with a length of feet and a width of feet?

Answer

The area of a rectangle is calculated by multiplying length times width.

$A=l\times w$

Given that the width is 6 feet and the height is 7, the product of 6 and 7 is 42.

$A=6\ \text{ft}\times 7\ \text{ft}$

$A=42\ \text{ft}^2$

Therefore, 42 is the correct answer.

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Question

If the area of a rectangle is 28 square inches and its width is 4 inches, what is the length in inches?

Answer

The area of a rectangle is equal to the width multiplied by the length, or:

$A=l\times w$

If the area of a rectangle is 28 inches and the width is 4 inches, then plugging this into the equation we would get:

$28=l\times4$

Divide both sides by 4 to solve.

$28\div4=4l\div4$

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Question

Ben is making a sandbox with a width of 4 feet and a length of 6 feet. What is the area of the sandbox?

Answer

The area of a rectangle is the width times the length.

$A=w\times l$

The width is 4 feet and the length is 6 feet. Because 4 times 6 is 24, the area is 24 square feet.

$A=4\text{ft}\times6\text{ft}$

$A=24\ \text{ft}^2$

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Question

Jerry has a mat with an area of 20 square feet and a length of 5 feet. What is the width of the mat in inches?

Answer

The area of a rectangle is the width times the length.

$A=w\times l$

Given that the area is 20 square feet and the length is 5 feet, the width would have to be 4 feet because 5 times 4 is 20.

$20\text{ft}^2=w\times5\text{ft}$

$w=\frac{20\text{ft}^2}{5\text{ft}}=4\text{ft}$

Given that the question asks for the width in inches, 4 should be multiplied by 12 (as there are 12 inches in a foot).

$4\text{ft}\times12\text{inches per foot}=48\text{in}$

This gives us a product of 48 inches, which is the width.

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Question

What is the area of a rectangle with a width of 6 inches and a length of 7 inches?

Answer

The area of a rectangle is equal to the length multiplied by the width. Since the width is 6 inches and the length is 7 inches, the area is equal to 6 times 7.

$A=l\times w$

$A=7\text{in}\times6\text{in}=42\text{in}^2$

The area is 42 square inches.

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Question

A rectangle has a length of 10 feet and a width of 1 foot. What is the area of the rectangle?

Answer

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

$A=l\times w$

Given that the length is 10 feet and that the width is 1 foot we can multiply to find the final area:

$A=10\text{ft}\times1\text{ft}=10\text{ft}^2$

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Question

If a rectangle has a perimeter of 40, a width of 4, and a length of 4x, what is the value of x?

Answer

The perimeter of a rectangle is equal to .

Thus, .

Add like terms:

Subtract 8 from both sides:

Divide both sides by 8:

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