Quadrilaterals - SSAT Middle Level Math

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Question

Note: Figure NOT drawn to scale

In the above diagram, $a = 14; \textrm{in} ,b=16; \textrm{in},h=10; \textrm{in}$

Give the area of the parallelogram.

Answer

The area of a parallelogram is its base multiplied by its height - represented by and here:

$A = bh = 16 \cdot 10 = 160$

Note that the value of is irrelevant.

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Question

Find the area of the following parallelogram:

Note: The formula for the area of a parallelogram is $A=b\times h$ .

Answer

The base of the parallelogram is 10, while the height is 5.

$A=b\times h$

$A=10\times5=50: in^2$

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Question

Find the area:

Answer

The area of a parallelogram can be determined using the following equation:

$\small A=bh$

Therefore,

$\small A=8\times3=24$

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Question

Find the area of the given parallelogram if .

Answer

In order to find the area of a parallelogram, we need to find the product of the base length and height.

Notice that only two of the given values were needed to slove this problem.

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Question

A given parallelogram has a base in length, a height in length, and a side of length opposite the height. What is the area of the parallelogram?

Answer

The formula for the area of a parallelogram is $A=b\times h$ , with base and height represented by and , respectively. Substituting values from the question:

$A=20:cm\times 16:cm$

$A=320:cm^{2}$

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Question

A parallelogram has a height of in length, a side of length opposite the height, and a base of . What is the area of the parallelogram?

Answer

Given base and height , $A=b\times h$ .

Substituting the values from our question:

$A=24:cm\times 10:cm$

$A=240:cm^{2}$

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Question

A parallelogram has a base of length , a height of length , and a side of length . What is the area of the parallelogram?

Answer

Given base and height , $A=b\times h$ .

Substituting the values from our question:

$A= 30:cm\times15:cm$

$A=450:cm^{2}$

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Question

Find the area of a parallelogram with a height of , a base of , and a side length of .

Answer

The area of a parallelogram with height and base can be found with the equation . Consequently:

$A=72:cm^{2}$

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Question

Find the area of a parallelogram with a height of , base of , and a side length of .

Answer

The area of a parallelogram with height and base can be found with the equation . Consequently:

$A=132:cm^{2}$

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Question

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

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.

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

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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?

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.

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Question

Give the area of the rectangle in the above diagram.

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.

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Question

Give the area of the rectangle in the above diagram.

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.

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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.

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.

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Question

The area of the following rectangle is . Solve for .

Answer

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

$A=l\times w$

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

$\frac{48}{3}=\frac{3x^2}{3}$

$\sqrt{16}=\sqrt{x^2}$

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Question

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

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

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Question

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

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

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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?

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.

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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?

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.

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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?

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 $1^{2} = 1$ .

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 $\frac{49}{16} : 1 = 49:16$ .

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