Rectangles

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SSAT Middle Level Quantitative › Rectangles

Questions 1 - 10

Rectangle

Give the area of the above rectangle in square feet.

$216 \textrm{ ft}^{2}$

$532\textrm{ ft}^{2}$

$576 \textrm{ ft}^{2}$

$33 \textrm{ ft}^{2}$

$66 \textrm{ ft}^{2}$

Explanation

Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:

$8 \textrm{ yd} \times 3 \textrm{ ft/yd} = 24 \textrm{ ft}$

$3 \textrm{ yd} \times 3 \textrm{ ft/yd} = 9 \textrm{ ft}$

Use the area formula, substituting :

$A = 24 \times 9 = 216$ square feet

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is $4 \times 1 = 4$ , and its area is $1^{2} = 1$ .

The perimeter of the first square is $\frac{7}{4} \times 4 = 7$ , and its sidelength is $7 \div 4 = \frac{7}{4}$ . The area of this square is therefore $\left (\frac{7}{4} \right )^{2} =\frac{49}{16}$ .

The ratio of the areas is therefore $\frac{49}{16} : 1 = 49:16$ .

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is $4 \times 1 = 4$ , and its area is $1^{2} = 1$ .

The ratio of the areas is therefore $\frac{49}{16} : 1 = 49:16$ .

Rectangle

Give the area of the above rectangle in square feet.

$216 \textrm{ ft}^{2}$

$532\textrm{ ft}^{2}$

$576 \textrm{ ft}^{2}$

$33 \textrm{ ft}^{2}$

$66 \textrm{ ft}^{2}$

Explanation

Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:

$8 \textrm{ yd} \times 3 \textrm{ ft/yd} = 24 \textrm{ ft}$

$3 \textrm{ yd} \times 3 \textrm{ ft/yd} = 9 \textrm{ ft}$

Use the area formula, substituting :

$A = 24 \times 9 = 216$ square feet

A rectangular table has a length of $2.2\ m$ and a width of $1.5\ m$ . Give the area of the table.

$33000\ cm^2$

$3300\ cm^2$

$3000\ cm^2$

$30000\ cm^2$

$330\ cm^2$

Explanation

We know that:

$Area=a\times b$

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$Area=2.2\ m \times 1.5\ m=(2.2\times 100\ cm)\times (1.5\times 100\ cm)=33000\ cm^2$

Order the following from least area to greatest area:

Figure A: A rectangle with length 10 inches and width 14 inches.

Figure B: A square with side length 1 foot.

Figure C: A triangle with base 16 inches and height 20 inches.

Explanation

Figure A has area $10 \times 14 = 140$ square inches.

Figure B has area $12 \times 12 = 144$ square inches, 1 foot being equal to 12 inches.

Figure C has area $\frac{1}{2} \times 16 \times 20 = 160$ square inches.

The figures, arranged from least area to greatest, are A, B, C.

A rectangular table has a length of $2.2\ m$ and a width of $1.5\ m$ . Give the area of the table.

$33000\ cm^2$

$3300\ cm^2$

$3000\ cm^2$

$30000\ cm^2$

$330\ cm^2$

Explanation

We know that:

$Area=a\times b$

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$Area=2.2\ m \times 1.5\ m=(2.2\times 100\ cm)\times (1.5\times 100\ cm)=33000\ cm^2$

The following question is about the Jones family wanting to buy square foot tiles for their rectangular basement. Their basement perimeter is 74 feet, with one of the sides being 15 feet long.

How many square foot titles are the Jones family needing to purchase in order to tile their basement?

Explanation

From the given information we know that the perimeter of the rectangular basement is 74 feet. We also know that one side of the rectangular basement is 15 feet. This means that the opposite side is also 15 feet long because the equivalent opposite sides rule of rectangles. In order to find the lengths of our other two sides of the rectangle, we need to subtract our two 15 feet sides from the perimeters 74 feet.

$74-30=44\ feet$ .

We know that the last two sides have to add up to 44 feet. Since the rules of rectangles say opposite sides are equivalent, we must take 44 feet and divide by the 2 sides. So 44 divided by 2 is 22 feet, meaning each side must be 22 feet. After adding up all the sides we can confirm that our perimeter is 74 feet.

Now we know all the sides of the rectangle, we are able to move to the next step, finding the area. We must find the area, because the tiles are square feet. So in order to find the area we must take the length of the rectangle and multiply it to the width.

$22\times 15= 330 ft^{2}$

Knowing the area of the rectangular basement we also know how many tile are needed to fill the basement for the Jones family. It is exactly 330 square feet tile needed.

Rectangle