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HiSET: Math : Perimeter and circumference

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Example Questions

Example Question #1 : Perimeter And Circumference

A five sided irregular polygon has sides of the following lengths:

$1,\ 4,\ 7,\ 8,\ \textup{and } 13$ $\displaystyle 1,\ 4,\ 7,\ 8,\ \textup{and } 13$

Find its perimeter.

Possible Answers:

$\displaystyle 23$

$\displaystyle 18$

$\displaystyle 20$

$\displaystyle 33$

$\displaystyle 1$

Correct answer:

$\displaystyle 33$

Explanation:

Perimeters can be calculated using the following formula.

$\displaystyle P=s_1+s_2+s_3...$

In this formula, the variable, $\displaystyle s$, represents a side of the polygon.

Substitute and solve.

$\displaystyle P=1+4+7+8+13$

P=33 $\displaystyle P=33$

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Example Question #81 : Hi Set: High School Equivalency Test: Math

The area of a square is $\displaystyle A$. In terms of $\displaystyle A$, give the perimeter of the square.

Possible Answers:

$\sqrt{2A}$ $\displaystyle \sqrt{2A}$

$2\sqrt{A}$ $\displaystyle 2\sqrt{A}$

$4A^{2}$ $\displaystyle 4A^{2}$

$4 \sqrt{A }$ $\displaystyle 4 \sqrt{A }$

$2A^{2}$ $\displaystyle 2A^{2}$

Correct answer:

$4 \sqrt{A }$ $\displaystyle 4 \sqrt{A }$

Explanation:

The length of one side of a square is equal to the square root of its area, so, if the area of a square is $\displaystyle A$, the common sidelength is $\sqrt{A}$ $\displaystyle \sqrt{A}$. Since a square comprises four sides of equal length, the perimeter is equal to four times this length, or $4\sqrt{A}$ $\displaystyle 4\sqrt{A}$.

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Example Question #1 : Perimeter And Circumference

The perimeter of a regular octagon is $16\sqrt{6}$ $\displaystyle 16\sqrt{6}$. Give the length of one side.

Possible Answers:

$\displaystyle 16$

$8\sqrt{6}$ $\displaystyle 8\sqrt{6}$

$4\sqrt{6}$ $\displaystyle 4\sqrt{6}$

$2\sqrt{6}$ $\displaystyle 2\sqrt{6}$

$\displaystyle 8$

Correct answer:

$2\sqrt{6}$ $\displaystyle 2\sqrt{6}$

Explanation:

A regular octagon has eight sides of equal length. Its perimeter is equal to the sum of the lengths of its sides, so the length of one side can be computed by dividing the perimeter by 8, as follows:

$l = \frac{P}{8}= \frac{16\sqrt{6}}{8} = \frac{16}{8} \sqrt{6}= 2\sqrt{6}$ $\displaystyle l = \frac{P}{8}= \frac{16\sqrt{6}}{8} = \frac{16}{8} \sqrt{6}= 2\sqrt{6}$,

the correct response.

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Example Question #1 : Perimeter And Circumference

Give the perimeter of a regular octagon in yards if the length of each side is $\displaystyle x$ feet.

Possible Answers:

$\frac{3}{8}x$ $\displaystyle \frac{3}{8}x$ yards

$\frac{8}{3}x$ $\displaystyle \frac{8}{3}x$ yards

24x $\displaystyle 24x$ yards

3x+8 $\displaystyle 3x+8$ yards

$\frac{1}{24}x$ $\displaystyle \frac{1}{24}x$ yards

Correct answer:

$\frac{8}{3}x$ $\displaystyle \frac{8}{3}x$ yards

Explanation:

The perimeter of a regular octagon - the sum of the lengths of its (eight congruent) sides - is eight times the common sidelength, so the perimeter of the octagon is $\displaystyle 8x$ feet. One yard is equivalent to three feet, so divide this by conversion factor 3 to get $\frac{8x}{3}$ $\displaystyle \frac{8x}{3}$ yards - the correct response.

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Example Question #1 : Perimeter And Circumference

Hexagon

Hexagon ABCDEF $\displaystyle ABCDEF$ is regular. Give the perimeter of Trapezoid ABEF $\displaystyle ABEF$.

Possible Answers:

$\displaystyle 15$

$\displaystyle 18$

$9+ 3\sqrt{3}$ $\displaystyle 9+ 3\sqrt{3}$

$9+ 3\sqrt{2}$ $\displaystyle 9+ 3\sqrt{2}$

$\displaystyle 12$

Correct answer:

$\displaystyle 15$

Explanation:

A regular hexagon can be divided into six equilateral triangles, as follows:

Hexagon

The perimeter of Trapezoid ABEF $\displaystyle ABEF$ can be seen to be $\displaystyle 3+3+(3+3)+3 = 15$.

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HiSET: Math : Perimeter and circumference

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #1 : Perimeter And Circumference

Example Question #81 : Hi Set: High School Equivalency Test: Math

Example Question #1 : Perimeter And Circumference

Example Question #1 : Perimeter And Circumference

Example Question #1 : Perimeter And Circumference

All HiSET: Math Resources

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