Quadrilaterals

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SSAT Middle Level Quantitative › Quadrilaterals

Questions 1 - 10

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Explanation

A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is .

A square is 9 feet long on each side. How many smaller squares, each 3 feet on a side can be cut out of the larger square?

Explanation

Each side can be divided into three 3-foot sections. This gives a total of $3\times3=9$ squares. Another way of looking at the problem is that the total area of the large square is 81 and each smaller square has an area of 9. Dividing 81 by 9 gives the correct answer.

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

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 square is 9 feet long on each side. How many smaller squares, each 3 feet on a side can be cut out of the larger square?

Explanation

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Explanation

A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is .

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

A square is 9 feet long on each side. How many smaller squares, each 3 feet on a side can be cut out of the larger square?

Explanation

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Explanation

A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is .

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