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Intermediate Geometry : Quadrilaterals

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Example Questions

Example Question #311 : Plane Geometry

Vt_custom_kite_series_int._geo

Using the kite shown above, find the length of side

Possible Answers:

18cm

11cm

21cm

9cm

$\frac{21}{2}cm$

Correct answer:

18cm

Explanation:

To find the missing side of this kite, work backwards using the formula:

p=2(a+b) , where and represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

58=2(11+b)

$\frac{58}{2}=11+b$

29=11+b

b=29-11=18

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Example Question #2 : How To Find The Length Of The Side Of A Kite

Vt_custom_kite_series_cont._

Using the kite shown above, find the length of side . (Note, the perimeter of this kite is equal to 2.5 feet).

Possible Answers:

$\frac{3}{4}ft$

1.5ft

4ft

1.25ft

$\frac{12}{5}in$

Correct answer:

$\frac{3}{4}ft$

Explanation:

To find the missing side of this kite, work backwards using the formula:

p=2(a+b) , where and represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

2.5 feet=2(0.5 foot+b)

$\frac{2.5}{2}=(0.5+b)$

1.25=0.5+b

$b=1.25-0.5=0.75=\frac{3}{4}$

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Example Question #1 : How To Find The Length Of The Side Of A Kite

Ms. Dunn has a kite shaped backyard with a perimeter of yards. One pair of adjacent sides of the kite-shaped backyard each have lengths of yard. What is the measurement for one of the other two sides of the kite-shaped backyard?

Possible Answers:

7yds

24yds

23yds

26yds

18yds

Correct answer:

23yds

Explanation:

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Example Question #1 : How To Find The Length Of The Side Of A Kite

A kite has a perimeter of 138 mm. One pair of adjacent sides of the kite have lengths of mm. What is the measurement for one of the other two sides of the kite?

Possible Answers:

105mm

69mm

26mm

36mm

79mm

Correct answer:

36mm

Explanation:

To find the missing side of this kite, work backwards using the formula:

p=2(a+b) , where and represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

138=2(33+b)

$\frac{138}{2}=33+b$

69=33+b

b=69-33=36

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

Kite_series_cont....

Using the above kite, find the length of side .

Possible Answers:

10.5in

12in

5in

11.5in

5.5in

Correct answer:

5.5in

Explanation:

To find the missing side of this kite, work backwards using the formula:

p=2(a+b) , where and represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

30=2(9.5+a)

30=19+2a

2a=30-19=11

$a=\frac{11}{2}=5.5$

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Example Question #1 : How To Find The Length Of The Side Of A Kite

The lengths of the non-adjacent sides of a kite have the ratio 4:1 . If the longer sides have a length of cm, what is the length of each of the shorter two sides?

Possible Answers:

3cm

$\frac{4}{12}cm$

19cm

1.5cm

4cm

Correct answer:

3cm

Explanation:

The sides have the ratio 4:1 , thus the longer sides must be times greater than the smaller sides.

Since the longer sides are cm, the shorter sides must be:

$12\div4=3$

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Example Question #151 : Quadrilaterals

A kite has a perimeter of 214 mm. One pair of adjacent sides of the kite have lengths of mm. What is the measurement for one of the other two sides of the kite?

Possible Answers:

107mm

41mm

55mm

53mm

71mm

Correct answer:

55mm

Explanation:

To find the missing side of this kite, work backwards using the formula:

p=2(a+b) , where and represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

214=2(52+b)

$\frac{214}{2}=(52+b)$

107=52+b

b=107-52=55

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Example Question #152 : Quadrilaterals

Kite_pic_custom_vt

Find the longest side of the kite that is shown above.

Possible Answers:

89in

93in

$\frac{91}{2}in$

83in

81in

Correct answer:

83in

Explanation:

To find the missing side of this kite, work backwards using the formula:

p=2(a+b) , where and represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

324=2(79+b)

$\frac{324}{2}=(79+b)$

162=(79+b)

b=162-79=83

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Example Question #153 : Quadrilaterals

A kite has a perimeter of $3\frac{1}{2}$ feet. One pair of adjacent sides of the kite have lengths of foot each. What is the measurement for one of the other two sides of the kite?

Possible Answers:

$\frac{1}{4}ft$

$\frac{3}{4}ft$

$1\frac{1}{4}ft$

$\frac{2}{3}ft$

$1\frac{1}{3}ft$

Correct answer:

$\frac{3}{4}ft$

Explanation:

To solve this problem use the formula p=2(a+b) , where and represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

$3\frac{1}{2}=2(1+b)$

$3\frac{1}{2}\div2=1+b$

Make the first fraction into an improper fraction. Then find the reciprocal of the denominator and switch the operation sign:

$3\frac{1}{2}\times\frac{1}{2}$

$\frac{7}{2}\times \frac{1}{2}=1+b$

$\frac{7}{4}=1+b$

$b=\frac{7}{4}-\frac{4}{4}=\frac{3}{4}$

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Example Question #11 : How To Find The Length Of The Side Of A Kite

Given: Regular Pentagon PENTA with center . Construct segments $\overline{CP}$ and $\overline{CN}$ to form Quadrilateral CPEN .

True or false: Quadrilateral CPEN is a kite.

Possible Answers:

False

True

Correct answer:

True

Explanation:

Below is regular Pentagon PENTA with center , a segment drawn from to each vertex - that is, each of its radii drawn.

Pentagon a

A kite is a quadrilateral with two sets of congruent adjacent sides, with the common length of one pair differing from that of the other. A regular polygon has congruent sides, so $\overline{EN} \cong \overline{EP}$ ; also, all radii of a regular polygon are congruent, so $\overline{CP} \cong \overline{CN}$ . It follows by definition that Quadrilateral CPEN is a kite.

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Intermediate Geometry : Quadrilaterals

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #311 : Plane Geometry

Example Question #2 : How To Find The Length Of The Side Of A Kite

Example Question #1 : How To Find The Length Of The Side Of A Kite

Example Question #1 : How To Find The Length Of The Side Of A Kite

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

Example Question #1 : How To Find The Length Of The Side Of A Kite

Example Question #151 : Quadrilaterals

Example Question #152 : Quadrilaterals

To find the missing side of this kite, work backwards using the formula:

Example Question #153 : Quadrilaterals

Example Question #11 : How To Find The Length Of The Side Of A Kite

All Intermediate Geometry Resources

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