Area and Perimeter - ISEE Upper Level Mathematics Achievement

What is the area of a triangle with $b=14$ and $h=5$ ?

$A=35$ . Compute half the product of the given base and height using the triangle area formula.
State the formula for the perimeter of a rectangle with length $l$ and width $w$ .

$P=2l+2w$ . The perimeter is twice the sum of the length and width, accounting for all four sides.
State the formula for the area of a circle with radius $r$ .

$A=pir^2$ . The area is $pi$ times the radius squared, quantifying the enclosed circular space.
What is the perimeter of a rectangle with $l=9$ and $w=4$ ?

$P=26$ . Apply the rectangle perimeter formula with given length and width values.
State the formula for the area of a square with side length $s$ .

$A=s^2$ . The area is the side length squared due to the equal sides forming a square region.
State the formula for the circumference of a circle with radius $r$ .

$C=2pir$ . The circumference is twice the product of $pi$ and the radius, measuring the boundary length.
What is the perimeter of a semicircle with radius $r=4$ ? (Include the diameter; leave in terms of $pi$ .)

$P=4pi+8$ . Add the semicircular arc length ( $pi r$ ) to the diameter ( $2r$ ) for the total perimeter.
What is the area of a parallelogram with $b=13$ and $h=4$ ?

$A=52$ . Multiply the given base and height using the parallelogram area formula.
What is the area of a regular hexagon if it is split into $6$ equilateral triangles of area $12$ each?

$A=72$ . Multiply the area of one equilateral triangle by six for the total hexagonal area.
What is the perimeter of a regular hexagon with side length $s=9$ ?

$P=54$ . Multiply the side length by six, as a regular hexagon has six equal sides.
State the formula for the area of a triangle with base $b$ and height $h$ .

$A=frac{1}{2}bh$ . The area is half the product of base and height, derived from dividing a parallelogram.
What is the circumference of a circle with diameter $d=10$ ? (Leave in terms of $pi$ .)

$C=10pi$ . Use the circumference formula with radius half of the given diameter.
What is the area of a square with side length $s=11$ ?

$A=121$ . Square the side length according to the square area formula.
State the formula for the area of a rhombus with diagonals $d_1$ and $d_2$ .

$A=frac{1}{2}d_1d_2$ . The area is half the product of the diagonals, which bisect each other at right angles.
What is the area of a trapezoid with $b_1=8$ , $b_2=12$ , and $h=5$ ?

$A=50$ . Average the bases, multiply by height, and halve using the trapezoid area formula.
What is the perimeter of a square with side length $s=7$ ?

$P=28$ . Multiply the side length by four using the square perimeter formula.
State the formula for the perimeter of a square with side length $s$ .

$P=4s$ . The perimeter is four times the side length since all sides are equal.
What is the area of a rectangle with $l=12$ and $w=3$ ?

$A=36$ . Multiply the given length and width using the rectangle area formula.
What is the area of a rhombus with diagonals $d_1=10$ and $d_2=8$ ?

$A=40$ . Take half the product of the given diagonals using the rhombus area formula.
State the formula for the area of a parallelogram with base $b$ and height $h$ .

$A=bh$ . The area is the product of base and height, as opposite sides are parallel.
What is the perimeter of a triangle with side lengths $5$ , $12$ , and $13$ ?

$P=30$ . Sum the given side lengths to find the total boundary of the triangle.
What is the area of a circle with radius $r=6$ ? (Leave in terms of $pi$ .)

$A=36pi$ . Apply the circle area formula by squaring the given radius and multiplying by $pi$ .
State the formula for the area of a rectangle with length $l$ and width $w$ .

$A=lw$ . The area is the product of length and width, representing the space enclosed.
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 is half the sum of the bases times height, averaging the parallel sides.

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