Area and Perimeter - ISEE Upper Level: Mathematics Achievement
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What is the perimeter of a triangle with side lengths $5$, $12$, and $13$?
What is the perimeter of a triangle with side lengths $5$, $12$, and $13$?
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$P=30$. Sum the given side lengths to find the total boundary of the triangle.
$P=30$. Sum the given side lengths to find the total boundary of the triangle.
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What is the area of a rhombus with diagonals $d_1=10$ and $d_2=8$?
What is the area of a rhombus with diagonals $d_1=10$ and $d_2=8$?
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$A=40$. Take half the product of the given diagonals using the rhombus area formula.
$A=40$. Take half the product of the given diagonals using the rhombus area formula.
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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 is half the sum of the bases times height, averaging the parallel sides.
$A=frac{1}{2}(b_1+b_2)h$. The area is half the sum of the bases times height, averaging the parallel sides.
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What is the perimeter of a regular hexagon with side length $s=9$?
What is the perimeter of a regular hexagon with side length $s=9$?
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$P=54$. Multiply the side length by six, as a regular hexagon has six equal sides.
$P=54$. Multiply the side length by six, as a regular hexagon has six equal sides.
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What is the area of a regular hexagon if it is split into $6$ equilateral triangles of area $12$ each?
What is the area of a regular hexagon if it is split into $6$ equilateral triangles of area $12$ each?
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$A=72$. Multiply the area of one equilateral triangle by six for the total hexagonal area.
$A=72$. Multiply the area of one equilateral triangle by six for the total hexagonal area.
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What is the perimeter of a semicircle with radius $r=4$? (Include the diameter; leave in terms of $pi$.)
What is the perimeter of a semicircle with radius $r=4$? (Include the diameter; leave in terms of $pi$.)
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$P=4pi+8$. Add the semicircular arc length ($pi r$) to the diameter ($2r$) for the total perimeter.
$P=4pi+8$. Add the semicircular arc length ($pi r$) to the diameter ($2r$) for the total perimeter.
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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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$A=50$. Average the bases, multiply by height, and halve using the trapezoid area formula.
$A=50$. Average the bases, multiply by height, and halve using the trapezoid area formula.
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What is the area of a parallelogram with $b=13$ and $h=4$?
What is the area of a parallelogram with $b=13$ and $h=4$?
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$A=52$. Multiply the given base and height using the parallelogram area formula.
$A=52$. Multiply the given base and height using the parallelogram area formula.
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What is the area of a triangle with $b=14$ and $h=5$?
What is the area of a triangle with $b=14$ and $h=5$?
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$A=35$. Compute half the product of the given base and height using the triangle area formula.
$A=35$. Compute half the product of the given base and height using the triangle area formula.
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What is the area of a circle with radius $r=6$? (Leave in terms of $pi$.)
What is the area of a circle with radius $r=6$? (Leave in terms of $pi$.)
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$A=36pi$. Apply the circle area formula by squaring the given radius and multiplying by $pi$.
$A=36pi$. Apply the circle area formula by squaring the given radius and multiplying by $pi$.
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What is the circumference of a circle with diameter $d=10$? (Leave in terms of $pi$.)
What is the circumference of a circle with diameter $d=10$? (Leave in terms of $pi$.)
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$C=10pi$. Use the circumference formula with radius half of the given diameter.
$C=10pi$. Use the circumference formula with radius half of the given diameter.
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What is the area of a square with side length $s=11$?
What is the area of a square with side length $s=11$?
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$A=121$. Square the side length according to the square area formula.
$A=121$. Square the side length according to the square area formula.
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What is the perimeter of a square with side length $s=7$?
What is the perimeter of a square with side length $s=7$?
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$P=28$. Multiply the side length by four using the square perimeter formula.
$P=28$. Multiply the side length by four using the square perimeter formula.
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What is the area of a rectangle with $l=12$ and $w=3$?
What is the area of a rectangle with $l=12$ and $w=3$?
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$A=36$. Multiply the given length and width using the rectangle area formula.
$A=36$. Multiply the given length and width using the rectangle area formula.
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What is the perimeter of a rectangle with $l=9$ and $w=4$?
What is the perimeter of a rectangle with $l=9$ and $w=4$?
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$P=26$. Apply the rectangle perimeter formula with given length and width values.
$P=26$. Apply the rectangle perimeter formula with given length and width values.
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State the formula for the area of a rhombus with diagonals $d_1$ and $d_2$.
State the formula for the area of a rhombus with diagonals $d_1$ and $d_2$.
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$A=frac{1}{2}d_1d_2$. The area is half the product of the diagonals, which bisect each other at right angles.
$A=frac{1}{2}d_1d_2$. The area is half the product of the diagonals, which bisect each other at right angles.
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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 is the product of base and height, as opposite sides are parallel.
$A=bh$. The area is the product of base and height, as opposite sides are parallel.
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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 is half the product of base and height, derived from dividing a parallelogram.
$A=frac{1}{2}bh$. The area is half the product of base and height, derived from dividing a parallelogram.
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State the formula for the area of a circle with radius $r$.
State the formula for the area of a circle with radius $r$.
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$A=pir^2$. The area is $pi$ times the radius squared, quantifying the enclosed circular space.
$A=pir^2$. The area is $pi$ times the radius squared, quantifying the enclosed circular space.
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State the formula for the circumference of a circle with radius $r$.
State the formula for the circumference of a circle with radius $r$.
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$C=2pir$. The circumference is twice the product of $pi$ and the radius, measuring the boundary length.
$C=2pir$. The circumference is twice the product of $pi$ and the radius, measuring the boundary length.
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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 is twice the sum of the length and width, accounting for all four sides.
$P=2l+2w$. The perimeter is twice the sum of the length and width, accounting for all four sides.
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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 is the side length squared due to the equal sides forming a square region.
$A=s^2$. The area is the side length squared due to the equal sides forming a square region.
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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 is four times the side length since all sides are equal.
$P=4s$. The perimeter is four times the side length since all sides are equal.
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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 is the product of length and width, representing the space enclosed.
$A=lw$. The area is the product of length and width, representing the space enclosed.
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