Perimeter and Area of Polygons - SSAT Upper Level Quantitative

What is the perimeter of a regular octagon with side length $s=7$ ?

$56$ . For a regular octagon, multiply the side length by eight to find the perimeter.
What is the area of a square with side length $s=12$ ?

$144$ . Square the side length to determine the area.
State the formula for the perimeter of a square with side length $s$ .

$P = 4s$ . The perimeter of a square is four times its side length.
State the formula for the area of a square with side length $s$ .

$A = s^2$ . The area of a square is the square of its side length.
What is the area of a triangle with base $b=14$ and height $h=6$ ?

$42$ . Take half the product of the base and height for the area.
What is the perimeter of a rectangle with $l=10$ and $w=3$ ?

$26$ . Add twice the length and twice the width to find the perimeter.
State the formula for the perimeter of a polygon with side lengths $s_1, s_2, \dots, s_n$ .

$P = s_1 + s_2 + \cdots + s_n$ . The perimeter is calculated by summing the lengths of all sides of the polygon.
State the formula for the area of a rhombus (or kite) with diagonals $d_1$ and $d_2$ .

$A = \frac{1}{2}d_1d_2$ . The area of a rhombus or kite is half the product of its diagonals.
What is the area of a trapezoid with $b_1=8$ , $b_2=12$ , and $h=5$ ?

$50$ . Average the bases, multiply by the height, and halve the result for the area.
What is the area of a $6$ by $4$ rectangle with a $2$ by $1$ rectangular hole removed?

$22$ . Subtract the area of the removed hole from the original rectangle's area.
State the formula for the area of a parallelogram with base $b$ and height $h$ .

$A = bh$ . The area of a parallelogram is the product of its base and height.
State the formula for the perimeter of a rectangle with length $l$ and width $w$ .

$P = 2l + 2w$ . The perimeter of a rectangle is twice the sum of its length and width.
State the formula for the area of a rectangle with length $l$ and width $w$ .

$A = lw$ . The area of a rectangle is found by multiplying its length by its width.
Identify the correct unit type for a polygon area measurement if side lengths are in centimeters.

$\text{cm}^2$ . Area measurements use square units corresponding to the linear units of the sides.
What is the perimeter of a polygon with side lengths $3, 5, 7, 9,$ and $6$ ?

$30$ . Sum all the given side lengths to compute the perimeter.
What is the area of a rectangle with $l=9$ and $w=4$ ?

$36$ . Multiply the length by the width to find the area.
State the formula for the area of a triangle with base $b$ and height $h$ .

$A = \frac{1}{2}bh$ . The area of a triangle is half the product of its base and height.
State the formula for the area of a regular polygon with apothem $a$ and perimeter $P$ .

$A = \frac{1}{2}aP$ . The area of a regular polygon is half the product of its apothem and perimeter.
What is the area of a rhombus with diagonals $d_1=10$ and $d_2=6$ ?

$30$ . Half the product of the diagonals gives the area.
What is the area of a regular polygon with apothem $a=9$ and perimeter $P=40$ ?

$180$ . Half the product of the apothem and perimeter yields the area.
State the formula for the area of a trapezoid with bases $b_1, b_2$ and height $h$ .

$A = \frac{1}{2}(b_1+b_2)h$ . The area of a trapezoid is half the product of the sum of its bases and its height.
What is the perimeter of a square with side length $s=15$ ?

$60$ . Multiply the side length by four to calculate the perimeter.
State the formula for the perimeter of a regular $n$ -gon with side length $s$ .

$P = ns$ . For a regular polygon, the perimeter is the product of the number of sides and the length of one side.
What is the area of a $10$ by $8$ rectangle if a right triangle with legs $10$ and $8$ is removed?

$40$ . Subtract the area of the removed triangle from the rectangle's area, leaving half the original.
What is the area of a parallelogram with base $b=11$ and height $h=5$ ?

$55$ . Multiply the base by the height to obtain the area.

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