Perimeter and Area of Polygons - SSAT Upper Level: Quantitative
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What is the perimeter of a square with side length $s=15$?
What is the perimeter of a square with side length $s=15$?
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$60$. Multiply the side length by four to calculate the perimeter.
$60$. Multiply the side length by four to calculate the perimeter.
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What is the area of a triangle with base $b=14$ and height $h=6$?
What is the area of a triangle with base $b=14$ and height $h=6$?
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$42$. Take half the product of the base and height for the area.
$42$. Take half the product of the base and height for the area.
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What is the area of a parallelogram with base $b=11$ and height $h=5$?
What is the area of a parallelogram with base $b=11$ and height $h=5$?
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$55$. Multiply the base by the height to obtain the area.
$55$. Multiply the base by the height to obtain the area.
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What is the area of a rhombus with diagonals $d_1=10$ and $d_2=6$?
What is the area of a rhombus with diagonals $d_1=10$ and $d_2=6$?
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$30$. Half the product of the diagonals gives the area.
$30$. Half the product of the diagonals gives the area.
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What is the area of a $6$ by $4$ rectangle with a $2$ by $1$ rectangular hole removed?
What is the area of a $6$ by $4$ rectangle with a $2$ by $1$ rectangular hole removed?
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$22$. Subtract the area of the removed hole from the original rectangle's area.
$22$. Subtract the area of the removed hole from the original rectangle's area.
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What is the area of a $10$ by $8$ rectangle if a right triangle with legs $10$ and $8$ is removed?
What is the area of a $10$ by $8$ rectangle if a right triangle with legs $10$ and $8$ is removed?
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$40$. Subtract the area of the removed triangle from the rectangle's area, leaving half the original.
$40$. Subtract the area of the removed triangle from the rectangle's area, leaving half the original.
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Identify the correct unit type for a polygon area measurement if side lengths are in centimeters.
Identify the correct unit type for a polygon area measurement if side lengths are in centimeters.
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$\text{cm}^2$. Area measurements use square units corresponding to the linear units of the sides.
$\text{cm}^2$. Area measurements use square units corresponding to the linear units of the sides.
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What is the perimeter of a regular octagon with side length $s=7$?
What is the perimeter of a regular octagon with side length $s=7$?
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$56$. For a regular octagon, multiply the side length by eight to find the perimeter.
$56$. For a regular octagon, multiply the side length by eight to find the perimeter.
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State the formula for the perimeter of a regular $n$-gon with side length $s$.
State the formula for the perimeter of a regular $n$-gon with side length $s$.
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$P = ns$. For a regular polygon, the perimeter is the product of the number of sides and the length of one side.
$P = ns$. For a regular polygon, the perimeter is the product of the number of sides and the length of one side.
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State the formula for the area of a rectangle with length $l$ and width $w$.
State the formula for the area of a rectangle with length $l$ and width $w$.
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$A = lw$. The area of a rectangle is found by multiplying its length by its width.
$A = lw$. The area of a rectangle is found by multiplying its length by its width.
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State the formula for the area of a square with side length $s$.
State the formula for the area of a square with side length $s$.
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$A = s^2$. The area of a square is the square of its side length.
$A = s^2$. The area of a square is the square of its side length.
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What is the area of a trapezoid with $b_1=8$, $b_2=12$, and $h=5$?
What is the area of a trapezoid with $b_1=8$, $b_2=12$, and $h=5$?
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$50$. Average the bases, multiply by the height, and halve the result for the area.
$50$. Average the bases, multiply by the height, and halve the result for the area.
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State the formula for the perimeter of a polygon with side lengths $s_1, s_2, \dots, s_n$.
State the formula for the perimeter of a polygon with side lengths $s_1, s_2, \dots, s_n$.
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$P = s_1 + s_2 + \cdots + s_n$. The perimeter is calculated by summing the lengths of all sides of the polygon.
$P = s_1 + s_2 + \cdots + s_n$. The perimeter is calculated by summing the lengths of all sides of the polygon.
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What is the area of a regular polygon with apothem $a=9$ and perimeter $P=40$?
What is the area of a regular polygon with apothem $a=9$ and perimeter $P=40$?
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$180$. Half the product of the apothem and perimeter yields the area.
$180$. Half the product of the apothem and perimeter yields the area.
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What is the perimeter of a polygon with side lengths $3, 5, 7, 9,$ and $6$?
What is the perimeter of a polygon with side lengths $3, 5, 7, 9,$ and $6$?
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$30$. Sum all the given side lengths to compute the perimeter.
$30$. Sum all the given side lengths to compute the perimeter.
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State the formula for the perimeter of a rectangle with length $l$ and width $w$.
State the formula for the perimeter of a rectangle with length $l$ and width $w$.
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$P = 2l + 2w$. The perimeter of a rectangle is twice the sum of its length and width.
$P = 2l + 2w$. The perimeter of a rectangle is twice the sum of its length and width.
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State the formula for the perimeter of a square with side length $s$.
State the formula for the perimeter of a square with side length $s$.
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$P = 4s$. The perimeter of a square is four times its side length.
$P = 4s$. The perimeter of a square is four times its side length.
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State the formula for the area of a triangle with base $b$ and height $h$.
State the formula for the area of a triangle with base $b$ and height $h$.
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$A = \frac{1}{2}bh$. The area of a triangle is half the product of its base and height.
$A = \frac{1}{2}bh$. The area of a triangle is half the product of its base and height.
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State the formula for the area of a parallelogram with base $b$ and height $h$.
State the formula for the area of a parallelogram with base $b$ and height $h$.
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$A = bh$. The area of a parallelogram is the product of its base and height.
$A = bh$. The area of a parallelogram is the product of its base and height.
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State the formula for the area of a trapezoid with bases $b_1, b_2$ and height $h$.
State the formula for the area of a trapezoid with bases $b_1, b_2$ and height $h$.
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$A = \frac{1}{2}(b_1+b_2)h$. The area of a trapezoid is half the product of the sum of its bases and its height.
$A = \frac{1}{2}(b_1+b_2)h$. The area of a trapezoid is half the product of the sum of its bases and its height.
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State the formula for the area of a rhombus (or kite) with diagonals $d_1$ and $d_2$.
State the formula for the area of a rhombus (or kite) with diagonals $d_1$ and $d_2$.
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$A = \frac{1}{2}d_1d_2$. The area of a rhombus or kite is half the product of its diagonals.
$A = \frac{1}{2}d_1d_2$. The area of a rhombus or kite is half the product of its diagonals.
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State the formula for the area of a regular polygon with apothem $a$ and perimeter $P$.
State the formula for the area of a regular polygon with apothem $a$ and perimeter $P$.
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$A = \frac{1}{2}aP$. The area of a regular polygon is half the product of its apothem and perimeter.
$A = \frac{1}{2}aP$. The area of a regular polygon is half the product of its apothem and perimeter.
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What is the area of a rectangle with $l=9$ and $w=4$?
What is the area of a rectangle with $l=9$ and $w=4$?
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$36$. Multiply the length by the width to find the area.
$36$. Multiply the length by the width to find the area.
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What is the perimeter of a rectangle with $l=10$ and $w=3$?
What is the perimeter of a rectangle with $l=10$ and $w=3$?
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$26$. Add twice the length and twice the width to find the perimeter.
$26$. Add twice the length and twice the width to find the perimeter.
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What is the area of a square with side length $s=12$?
What is the area of a square with side length $s=12$?
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$144$. Square the side length to determine the area.
$144$. Square the side length to determine the area.
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