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ACT Math : Plane Geometry

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Example Questions

Example Question #44 : Quadrilaterals

Kite vt act

Using the kite shown above, find the perimeter measurement.

Possible Answers:

Correct answer:

Explanation:

A kite must have two sets of equivalent sides. Since we know that this kite has a side length of and another side length of , each of these two sides must have one equivalent side. Therefore, the perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(12+17)

p=2(29)=58

Note: the correct solution can also be found by:

p=12+12+17+17=24+34=58

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Example Question #45 : Quadrilaterals

Kite vt act

Using the kite shown above, find the perimeter measurement.

Possible Answers:

107.5

75.5

105

87.5

Correct answer:

105

Explanation:

A kite must have two sets of equivalent sides. Since we know that this kite has a side length of and another side length of $\frac{35}{2}=17.5$ , each of these two sides must have one equivalent side. Therefore, the perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(35+17.5)

p=2(52.5)=105

Note: the correct solution can also be found by:

p=35+35+17.5+17.5=70+35=105

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Example Question #281 : Act Math

Kite vt act

Using the kite shown above, find the perimeter measurement.

Possible Answers:

10.25

17.5

17.25

20.25

20.5

Correct answer:

20.5

Explanation:

A kite must have two sets of equivalent sides. Since we know that this kite has a side length of and another side length of 3.25 , each of these two sides must have one equivalent side. Therefore, the perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(7+3.25)

p=2(10.25)=20.5

Additionally, the correct solution can also be found by:

p=7+7+3.25+3.25=14+6.5=20.5

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Example Question #46 : Quadrilaterals

Kite vt act

Using the kite shown above, find the perimeter measurement.

Possible Answers:

130

147

Correct answer:

130

Explanation:

By definition a kite must have two sets of equivalent sides. Since we know that this kite has a side length of and another side with a length of , each of these two sides must have one equivalent side. Therefore, the perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(26+39)

p=2(65)=130

Note: the correct solution can also be found by:

p=26+26+39+39=52+78=130

The original formula used in this solution is an application of the Distributive Property: 2a+2b=2(a+b)

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Example Question #1 : How To Find The Perimeter Of Kite

A kite has a side length of and another side length of . Find the perimeter of the kite.

Possible Answers:

Correct answer:

Explanation:

The perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(40+8)

p=2(48)=96

Note: the correct solution can also be found by:

p=8+8+40+40=16+80=96

The original formula used in this solution is an application of the Distributive Property: 2a+2b=2(a+b)

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Example Question #48 : Quadrilaterals

A kite has a side length of $\frac{3}{4} \textup{feet}$ and another side length of $\frac{1}{3}\textup{feet}$ . Find the perimeter of the kite.

Possible Answers:

$24\textup{ inches}$

$13\textup{ inches}$

$17\textup{ inches}$

$9\textup{ inches}$

$26\textup{ inches}$

Correct answer:

$26\textup{ inches}$

Explanation:

A kite must have two sets of equivalent sides. Since we know that this kite has a side length of $\frac{3}{4}\textup{feet}$ and another side with a length of $\frac{1}{3}\textup{feet}$ , each of these two sides must have one equivalent side.

The perimeter of this kite can be found by applying the formula:

p=2(a+b)

Additionally, this problem first requires you to convert each side length from feet to inches.

$\frac{3}{4}\textup{ft}=\frac{3}{4}\times\frac{3}{3}=\frac{9}{12}=9\textup{ inches}$

$\frac{1}{3}\textup{ft}=\frac{1}{3}\times \frac{4}{4}=\frac{4}{12}=4\textup{ inches}$

The solution is:

p=2(9+4)

p=2(13)=26

Note: the correct solution can also be found by:

p=9+9+4+4=18+8=26

The original formula used in this solution is an application of the Distributive Property: 2a+2b=2(a+b)

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Example Question #281 : Act Math

A kite has a side length of and another side length of 13.5 . Find the perimeter of the kite.

Possible Answers:

33.5

53.5

270

Correct answer:

Explanation:

By definition a kite must have two sets of equivalent sides. Since we know that this kite has a side length of and another side with a length of 13.5 , each of these two sides must have one equivalent side.

The perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(20+13.5)

p=2(33.5)=67

Note: the correct solution can also be found by:

p=20+20+13.5+13.5=40+27=67

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Example Question #51 : Kites

A kite has a side length of $15\textup{ inches}$ and another side length of $30\textup{ inches}$ . Find the perimeter of the kite.

Possible Answers:

$45\textup{ inches}$

$7.5\textup{ feet}$

$87\textup{ inches}$

$90 \textup{ cm}$

$12\textup{ feet}$

Correct answer:

$7.5\textup{ feet}$

Explanation:

The perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(15+30)

$p=2(45)=90\textup{ inches}$

Note, though, that $90\textup{ inches}$ does not appear as an answer choice. Thus, convert $90\textup{ inches}$ into $\textup{feet}$ by: $90\div12=7.5\textup{ feet}$

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Example Question #51 : Quadrilaterals

A kite has a side length of $88\textup{mm}$ and another side length of $36\textup{mm}$ . Find the perimeter of the kite.

Possible Answers:

$209\textup{cm}$

$264\textup{mm}$

$176\textup{mm}$

$248\textup{mm}$

$209\textup{mm}$

Correct answer:

$248\textup{mm}$

Explanation:

a kite must have two sets of equivalent sides. Since we know that this kite has a side length of $88\textup{mm}$ and another side with a length of $36\textup{mm}$ , each of these two sides must have one equivalent side.

The perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(88+36)

$p=2(124)=248\textup{mm}$

Note: the correct solution can also be found by:

p=88+88+36+36=176+72=248

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Example Question #52 : Quadrilaterals

A kite has a side length of $12\textup{cm}$ and another side length of $16\textup{cm}$ . Find the perimeter of the kite.

Possible Answers:

$24\textup{cm}$

$96\textup{in}$

$60\textup{cm}$

$56\textup{cm}$

$90\textup{cm}$

Correct answer:

$56\textup{cm}$

Explanation:

A kite must have two sets of equivalent sides. Since we know that this kite has a side length of and another side length of , each of these two sides must have one equivalent side.

The perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(12+16)

$p=2(28)=56\textup{cm}$

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ACT Math : Plane Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #44 : Quadrilaterals

Example Question #45 : Quadrilaterals

Example Question #281 : Act Math

Example Question #46 : Quadrilaterals

Example Question #1 : How To Find The Perimeter Of Kite

Example Question #48 : Quadrilaterals

Example Question #281 : Act Math

Example Question #51 : Kites

Example Question #51 : Quadrilaterals

Example Question #52 : Quadrilaterals

All ACT Math Resources

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