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ACT Math : Quadrilaterals

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #4 : How To Find The Length Of The Side Of A Kite

A kite has two adjacent sides both with a measurement of . The perimeter of the kite is . Find the length of the sum of the remaining two sides.

Possible Answers:

Correct answer:

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided.

To find the sum of the remaining two sides:

88=18+18+2(side) 188=40+40+2(side) , where side= one of the two missing sides.

88=36+2(side)

2(side)=88-36=52

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Example Question #5 : How To Find The Length Of The Side Of A Kite

Kite vt act

The kite shown above has two adjacent sides both with a measurement of . The perimeter of the kite is . Find the sum of the remaining two sides.

Possible Answers:

14.5

7.5

Correct answer:

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. This problem also provides the perimeter measurement of the kite. Therefore, use the information that is provided to find the difference between the perimeter and the sum of the congruent adjacent sides provided in the question.

To find the sum of the remaining two sides:

38=12+12+2(side) , where side= one of the two missing sides.

38=24+2(side)

2(side)=38-24=14

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Example Question #6 : How To Find The Length Of The Side Of A Kite

A kite has two adjacent sides both with a measurement of $15\textup{ inches}$ . The perimeter of the kite is $55\textup{ inches}$ . Find the length of one of the remaining two sides.

Possible Answers:

$12.5\textup{ inches}$

$15\textup{ inches}$

$7.5\textup{ inches}$

$25\textup{ inches}$

$30\textup{ inches}$

Correct answer:

$12.5\textup{ inches}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

55=15+15+2(side) , where side= one of the two missing sides.

55=30+2(sides)

2(sides)=55-30 = 25

$side=\frac{25}{2}=12.5$

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Example Question #7 : How To Find The Length Of The Side Of A Kite

Kite vt act

Using the kite shown above, find the length of side .

Possible Answers:

$4\textup{ ft}$

$4.5\textup{ ft}$

$1.5\textup{ ft}$

$2\textup{ ft}$

$2.5\textup{ ft}$

Correct answer:

$2\textup{ ft}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided.

The solution is:

13=4.5+4.5+2(side) , where side= one of the two missing sides.

13=9+2(sides)

2(sides)=13-9 = 4
Since the remaining two sides have a total length of ft, side must be $\frac{4}{2}=2$

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Example Question #8 : How To Find The Length Of The Side Of A Kite

A kite has two adjacent sides both with a measurement of $35\textup{ mm}$ . The perimeter of the kite is $90\textup{ mm}$ . Find the length of one of the remaining two sides.

Possible Answers:

$20\textup{mm}$

$5\textup{mm}$

$\sqrt{10}\textup{mm}$

$10\textup{mm}$

$15\textup{mm}$

Correct answer:

$10\textup{mm}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

90=35+35+2(side) , where side= one of the two missing sides.

90=70+2(sides)

2(sides)=90-70 = 20

$side=\frac{20}{2}=10$

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Example Question #9 : How To Find The Length Of The Side Of A Kite

A kite has two adjacent sides both with a measurement of $40\textup{mm}$ . The perimeter of the kite is $188\textup{mm}$ . Find the length of the sum of the remaining two sides.

Possible Answers:

$148\textup{mm}$

$108\textup{mm}$

$112\textup{mm}$

$59\textup{mm}$

$54\textup{mm}$

Correct answer:

$108\textup{mm}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided.

The solution is:

188=40+40+2(side) , where side= one of the two missing sides.

188=80+2(sides)

2(sides)=188-80 = 108

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Example Question #10 : How To Find The Length Of The Side Of A Kite

A kite has two adjacent sides both with a measurement of $55\textup{mm}$ . The perimeter of the kite is $200\textup{mm}$ . Find the length of one of the remaining two sides.

Possible Answers:

$55\textup{mm}$

$52.5\textup{mm}$

$90\textup{mm}$

$110\textup{mm}$

$45\textup{mm}$

Correct answer:

$45\textup{mm}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

200=55+55+2(side) , where side= one of the two missing sides.

200=110+2(sides)

2(sides)=200-110 = 90

$side=\frac{90}{2}=45$

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Example Question #31 : Kites

A kite has two adjacent sides both with a measurement of 11.5 . The perimeter of the kite is . Find the length of the sum of the remaining two sides.

Possible Answers:

11.75

22.5

Correct answer:

Explanation:

This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided.

The solution is:

45=11.5+11.5+2(side) , where side= one of the two missing sides.

45=23+2(sides)

2(sides)=45-23 = 22

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Example Question #32 : Kites

A kite has two adjacent sides both with a measurement of $\frac{3}{4}\textup{mm}$ . The perimeter of the kite is $28\textup{ inches}$ . Find the length of one of the remaining two sides.

Possible Answers:

$3.5\textup{ inches}$

$5\textup{ inches}$

$\frac{5}{12}\textup{ inch}$

$10\textup{ inches}$

$\frac{10}{12}\textup{ft}$

Correct answer:

$5\textup{ inches}$

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

$\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}=9 in.$

The solution is:

28=9+9+2(side) , where side= one of the two missing sides.

28=18+2(sides)

2(sides)=28-18 = 10

$side=\frac{10}{2}=5$

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

A kite has two shorter sides and two longer sides. Each of the shorter sides has a length of 19 and each of the longer sides has a length of 25. What is the perimeter of the kite?

Possible Answers:

100

Correct answer:

Explanation:

Remember that a kite has two adjacent sets of shorter sides as well as two adjacent sets of longer sides.

Use the formula for perimeter of a kite:

$P=2s_{1}+2s_{2}$

Where is the perimeter, s_1 is the length of the shorter sides, and s_2 is the length of the longer sides.

$P=(2\times 19)+(2\times 25)=88$

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ACT Math : Quadrilaterals

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #4 : How To Find The Length Of The Side Of A Kite

Example Question #5 : How To Find The Length Of The Side Of A Kite

Example Question #6 : How To Find The Length Of The Side Of A Kite

Example Question #7 : How To Find The Length Of The Side Of A Kite

Example Question #8 : How To Find The Length Of The Side Of A Kite

Example Question #9 : How To Find The Length Of The Side Of A Kite

Example Question #10 : How To Find The Length Of The Side Of A Kite

Example Question #31 : Kites

Example Question #32 : Kites

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

All ACT Math Resources

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