Rectangles - SSAT Middle Level Quantitative

Card 1 of 248

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

What is the area of a rectangle with length $14\ cm$ and width $12\ cm$ ?

Tap to reveal answer

Answer

The formula for the area, , of a rectangle when we are given its length, , and width, , is .

To calculate this area, just multiply the two terms.

$A = 14\ cm * 12\ cm = 168; $cm^{2}$$

← Didn't Know|Knew It →

Question

Steve's bedroom measures 20' by 18' by 8' high. He wants to paint the ceiling and all four walls using a paint that gets 360 square feet of coverage per gallon. A one-gallon can of the paint Steve wants costs $36.00; a one-quart can costs $13.00. What is the least amount of money that Steve can expect to spend on paint in order to paint his room?

Tap to reveal answer

Answer

Two of the walls have area $20 \cdot 8 = 160;\textrm{in}^{2}$ ; two have area $18 \cdot 8 = 144;\textrm{in}^{2}$ ; the ceiling has area $20 \cdot 18 = 360;\textrm{in}^{2}$ .

Therefore, the total area Steve wants to cover is

$A = 160 + 160 + 144 + 144 + 360 =968 ; \textrm{in}^{2}$

Divide 968 by 360 to get the number of gallons Steve needs to paint his bedroom:

$968 \div 360 \approx 2.7$

Since $2 \frac{1}{2} < 2.7 < 2\frac{3}{4}$ , Steve needs to purchase either two gallon cans and three quart cans, or three gallon cans.

The first option will cost him $36 \cdot2 + 13 \cdot3 = \$111$ ; the second option will cost him $36 \cdot3 = \$108$ . The latter is the more economical option.

← Didn't Know|Knew It →

Question

Give the area of the rectangle in the above diagram.

Tap to reveal answer

Answer

The area of a rectangle is the product of its length and its height:

$12.6 \cdot6.4 = 80.64$

The rectangle has a perimeter of 80.64 square centimeters.

← Didn't Know|Knew It →

Question

Give the area of the rectangle in the above diagram.

Tap to reveal answer

Answer

The area of a rectangle is the product of its length and its width:

$7 $\frac{1}{2}$ \cdot 5 $\frac{3}{5}$$

$=\frac{7 \cdot 2 + 1}{2}$ \cdot $\frac{5\cdot 5 + 3}{5}$$

$=\frac{15}{2}$ \cdot $\frac{28}{5}$ =\frac{3}{1}$ \cdot $\frac{14}{1}$ = 42$

The area of the rectangle is 42 square inches.

← Didn't Know|Knew It →

Question

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.

Tap to reveal answer

Answer

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.

← Didn't Know|Knew It →

Question

The area of the following rectangle is . Solve for .

Tap to reveal answer

Answer

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

$A=l\times w$

$48=3x\times $x=3x^2$$

← Didn't Know|Knew It →

Question

Give the surface area of the above box in square inches.

Tap to reveal answer

Answer

Use the surface area formula, substituting :

$A = 2 \cdot 22 \cdot 12 + 2 \cdot 22 \cdot 12 + 2\cdot 12\cdot 12$

square inches

← Didn't Know|Knew It →

Question

Give the surface area of the above box in square centimeters.

Tap to reveal answer

Answer

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

$0.9 \times 100 = 90$ centimeters

$0.6 \times 100 = 60$ centimeters

Use the surface area formula, substituting :

$A = 2 \cdot 90 \cdot 60 + 2\cdot 90 \cdot 60 + 2 \cdot 60 \cdot 60$

square centimeters

← Didn't Know|Knew It →

Question

Above is a figure that comprises a red square and a white rectangle. The ratio of the length of the white rectangle to the sidelength of the square is . What percent of the entire figure is red?

Tap to reveal answer

Answer

To make this easier, we will assume that the rectangle has length 5 and the square has sidelength 3. Then the area of the entire figure is

$(3 + 5) \times 3 = 24$ ,

and the area of the square is

$3 \times 3 = 9$

The square, therefore, takes up

$$\frac{9}{24}$ \times 100 = $\frac{900}{24}$ = 37.5 %$

of the entire figure.

← Didn't Know|Knew It →

Question

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?

Tap to reveal answer

Answer

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.

← Didn't Know|Knew It →

Question

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?

Tap to reveal answer

Answer

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 .

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$ .

← Didn't Know|Knew It →

Question

Give the area of the above rectangle in square feet.

Tap to reveal answer

Answer

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

← Didn't Know|Knew It →

Question

The rectangle above is inches long and inches wide. What is the area of the rectangle?

Note: Figure not drawn to scale.

Tap to reveal answer

Answer

The area of the rectangle is $50: $in^{2}$$ . In order to find the area of a rectangle, multiply the length (5 inches) by the width (10 inches). The answer is in units2 because the area, by definition, is the number of square units that cover the inside of a figure.

← Didn't Know|Knew It →

Question

Which of the following is equal to the area of a rectangle with length feet and width $1 $\frac{1}{2}$$ feet?

Tap to reveal answer

Answer

Multiply each dimension by 12 to convert from feet to inches:

$3 \times 12 = 36 \textrm{ in}$

$1 $\frac{1}{2}$ \times 12 = 18 \textrm{ in}$

Now multiply this length and width to get the area:

$36 \times 18 = 648 \textrm{ $in}^{2}$$

← Didn't Know|Knew It →

Question

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its surface area in square feet.

Tap to reveal answer

Answer

Divide each dimension in inches by 12 to convert from inches to feet:

$L = 24 \div 12 = 2$ feet

$W = 18 \div 12 = 1 $\frac{1}{2}$ = $\frac{3}{2}$$ feet

$H = 15 \div 12 = 1 $\frac{1}{4}$ = $\frac{5}{4}$$ feet

Now, substitute in the surface area formula:

$A = 2\cdot 2 \cdot $\frac{3}{2}$ + 2 \cdot $\frac{3}{2}$\cdot $\frac{5}{4}$ + 2\cdot 2 \cdot $\frac{5}{4}$$

$A =6 + $\frac{15}{4}$ + 5$

$A =6 + 3 $\frac{3}{4}$ + 5$

$A $=14$\frac{3}{4}$ft^{2}$$

← Didn't Know|Knew It →

Question

If a cereal box has a volume of 40 cubic inches, a width of 2 inches, and a height of 5 inches, what is its length?

Tap to reveal answer

Answer

The formula for the volume of a rectangular solid is .

Use the provided information from the question in the above formula and solve for the length.

Therefore, the length of the box is 4 inches. In answering this question, it is important to look at the units before selecting an answer. It is easy to be tricked into thinking that because the total answer is in cubic inches that it may be necessary to have square inches, but when multiplying three values, each with inches as their units, the units of the product will be cubic inches.

← Didn't Know|Knew It →

Question

Which of the following is equal to the area of a rectangle with length meters and width meters?

Tap to reveal answer

Answer

Multiply each dimension by to convert meters to centimeters:

$4.3 \times 100 = 430$

$3.5 \times 100 = 350$

Multiply these dimensions to get the area of the rectangle in square centimeters:

$430 \times 350 = 150,500\textrm{ $cm}^{2}$$

← Didn't Know|Knew It →

Question

Which of the following is equal to the area of a rectangle with length 27 inches and width 15 inches?

Tap to reveal answer

Answer

Divide each dimension by 12 to convert from inches to feet:

$27 \div 12 = 2.25$

$15 \div 12 = 1.25$

Multiply length by width:

$2.25 \times 1.25 = 2.8125$ square feet

← Didn't Know|Knew It →

Question

Which of the following is equal to the area of a rectangle with length 250 centimeters and width 140 centimeters?

Tap to reveal answer

Answer

Divide each dimension by 100 to convert centimeters to meters:

$250 \div 100 = 2.5$

$140 \div 100 = 1.4$

Multiply length by width:

$2.5 \times 1.4 = 3.5$ square meters

← Didn't Know|Knew It →

Question

A hectare is a unit of area equal to 10,000 square meters.

A rectangular plot of land measures 1,400 meters by 800 meters. Give the area of this plot in hectares.

Tap to reveal answer

Answer

Multiply length times width to get the area in square meters:

$A = 1,400 \times 800 = 1,120,000$ square meters

Divide by 10,000 to convert to hectares:

$1,120,000 \div 10,000 = 112$ hectares

← Didn't Know|Knew It →

0

Knew It