Quadrilaterals - ISEE Middle Level Quantitative Reasoning

Card 0 of 2125

Question

The area of a square is ?

Answer

The area of a square is the side length squared not the side length times .

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Question

If you are given one side length of a square, you can find the area with that information.

Answer

To find the area of a square, you multiple . But with a square all the sides are equal so the equation really is or the side length squared. Since you are given the side length, you can find the area.

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Question

Each side of a square is units long. Which is the greater quantity?

(A) The area of the square

(B)

Answer

The area of a square is the square of its side length:

Using the side length from the question:

$A=\left ( 5t\right ) ^{2} = 5 ^{2} \cdot t ^{2} = 25t ^{2}$

However, it is impossible to tell with certainty which of $25t ^{2}$ and is greater.

For example, if ,

$25t ^{2} = 25 \cdot 2^{2} = 25 \cdot4 = 100$

and

$25t = 25 \cdot 2 = 50$

so $25t ^{2} > 25t$ if .

But if $t = \frac{1}{5}$ ,

$25t ^{2}=25 \cdot \left ( \frac{1}{5} \right )^{2} = 25 \cdot \frac{1}{25} = 1$

and

$25t =25 \cdot \frac{1}{5} = 5$

so $25t ^{2} < 25t$ if $t = \frac{1}{5}$ .

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Question

What is the perimeter of a square with area 196 square inches?

Answer

A square with area 196 square inches has sidelength $\sqrt{196} = 14$ inches, and therefore has perimeter $4 \cdot 14 = 56$ inches

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Question

If a square has sides measuring $\small \small \frac{1}{8}$ , what is the perimeter of the square, in simplest form?

Answer

To find the perimeter of a square, you must add together all the sides. In this case, we are adding $\small \frac{1}{8}$ four times.

$\small \frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}=\frac{4}{8}$

Since all of the denominators are the same, there is no need to find a commond denominator, so we add together the numerators. This gives us $\small \frac{4}{8}$ .

Since both the numerator and denomator are divisible by four, we must simplify this fraction.

$\small \frac{4/4}{8/4}= \frac{1}{2}$

The perimeter of the square is $\small \small \frac{1}{2}$ .

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Question

The sum of the lengths of three sides of a square is one foot. Give the perimeter of the square in inches.

Answer

A square has four sides of the same length.

One foot is equal to twelve inches; since the sum of the lengths of three of the congruent sides is twelve inches, each side measures

$12 \div 3 = 4$ inches.

The perimeter is

$4 \times 4 = 16$ inches.

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Question

A square has perimeter one yard. Which is the greater quantity?

(A) The length of one side of the square

(B) 8 inches

Answer

One yard is equal to 36 inches. A square has four sides of equal length, so one side of the square has length

$36 \div 4 = 9$ inches.

Since , (A) is greater.

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Question

A square has perimeter five meters. Which is the greater quantity?

(A) 1,250 millimeters

(B) The length of one side of the square

Answer

One meter is equal to 1,000 millimeters, so the square has perimeter

$5 \times 1,000 = 5,000$ millimeters.

A square has four sides of equal length, so one side of the square has length

$5,000 \div 4 = 1,250$ millimeters.

The quantities are equal.

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Question

A square has perimeter one meter. Which is the greater quantity?

(A) 250 centimeters

(B) The length of one side of the square

Answer

One meter is equal to 100 centimeters.

A square has four sides of equal length, so we will need to divide by 4 to find the length of one side.

$P\div4=s$

$100cm \div 4 = 25cm$

, so (A) is greater

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Question

A square lot has perimeter one mile. Which is the greater quantity?

(A) 1,320 feet

(B) The length of one side of the square

Answer

One mile is equal to 5,280 feet. A square has four sides of equal length, so one side of the square has length

$5,280 \div 4 = 1,320$ feet.

The quantities are equal.

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Question

Each side of a square is units long. Which is the greater quantity?

(A)

(B) The perimeter of the square

Answer

The perimeter of a square is four times its side length:

$P=4\times4t$

Since the perimeter is equal to , (A) and (B) are equal.

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Question

The sum of the lengths of three sides of a square is 9,000 centimeters. Give its perimeter in meters.

Answer

100 centimeters are equal to one meter, so 9,000 centimeters are equal to

$9,000 \div 100 = 90$ meters.

A square has four sides of the same length. Since the sum of the lengths of three of the congruent sides is 9,000 centimeters, or 90 meters, each side measures

$90 \div 3 = 30$ meters.

The perimeter is four times this, which is

$30 \times 4 = 120$ meters.

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Question

What is the length of a rectangular room with a perimeter of and a width of

Answer

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

$\frac{36}{2}=\frac{2l}{2}$

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Question

What is the length of a rectangular room with a perimeter of and a width of

Answer

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

$\frac{64}{2}=\frac{2l}{2}$

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Question

What is the length of a rectangular room with a perimeter of and a width of

Answer

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

$\frac{66}{2}=\frac{2l}{2}$

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Question

What is the length of a rectangular room with a perimeter of and a width of

Answer

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

$\frac{36}{2}=\frac{2l}{2}$

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Question

What is the length of a rectangular room with a perimeter of and a width of

Answer

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

$\frac{32}{2}=\frac{2l}{2}$

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Question

What is the length of a rectangular room with a perimeter of and a width of

Answer

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

$\frac{28}{2}=\frac{2l}{2}$

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Question

What is the length of a rectangular room with a perimeter of and a width of

Answer

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

$\frac{30}{2}=\frac{2l}{2}$

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Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=3\times 3$ $A=2\times 1$

To find our final answer, we need to add the areas together.

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