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Intermediate Geometry : Kites

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Example Question #21 : Kites

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:

True

False

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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Example Question #22 : Kites

Kite_series_2

Using the kite shown above, find the length of side

Possible Answers:

Correct answer:

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Thus, the length of side b=a+5 .

Since, , must equal 7+5=12 .

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Example Question #23 : Kites

Kite_series_2

What is the length of side

Possible Answers:

Correct answer:

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides. In this kite the two adjacent sides which are congruent are those at the top of the kite and then likewise, the two that are connected at the bottom of the kite.

Thus, must equal .

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Example Question #21 : Kites

A kite has one set of equivalent sides each with a measurement of . Additionally, the kite has a perimeter of 48. Find the length for one of the other two sides of the kite.

Possible Answers:

Correct answer:

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula:

perimeter=2(a+b) , where and are the lengths of opposite sides of the kite and solve for .

48=2(9+b)

$\frac{48}{2}=(9+b)$

24=9+b

b=24-9=15

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Example Question #21 : Kites

A kite has one set of equivalent sides each with a measurement of . Additionally, the kite has a perimeter of 88. Find the length for one of the other two sides of the kite.

Possible Answers:

Correct answer:

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula:

perimeter=2(a+b) , where and are the lengths of opposite sides of the kite and solve for .

88=2(a+31)

$a+31=\frac{88}{2}$

a=44-31=13

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Example Question #26 : Kites

A kite has one set of equivalent sides each with a measurement of cm. Additionally, the kite has a perimeter of 450 cm. Find the length for one of the other two sides of the kite.

Possible Answers:

262cm

133cm

231cm

133in

131cm

Correct answer:

131cm

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula:

perimeter=2(a+b) , where and are the lengths of opposite sides of the kite and solve for .

450=2(94+b)

$\frac{450}{2}=94+b$

225=94+b

b=225-94=131

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Example Question #27 : Kites

A kite has one set of equivalent sides each with a measurement of $\frac{2}{4}$ foot. Additionally, the kite has a perimeter of 4.5 feet. Find the length for one of the other two sides of the kite.

Possible Answers:

1.25 feet

1.75 feet

0.5foot

$\frac{3}{4} foot$

2.25 feet

Correct answer:

1.75 feet

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula: perimeter=2(a+b) , where and are the lengths of opposite sides of the kite and solve for .

4.5=2(0.5+b)

$0.5+b=\frac{4.5}{2}=2.25$

b=2.25-0.5=1.75

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Example Question #28 : Kites

Kite_series_2

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

Possible Answers:

8.5in

5.5 in

16 in

5 in

8in

Correct answer:

5.5 in

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula: perimeter=2(a+b) , where and are the lengths of opposite sides of the kite and solve for .

43=2(a+16)

$a+16=\frac{43}{2}$

a+16=21.5

a=21.5-16=5.5

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Example Question #29 : Kites

Kite_series_2

Using the kite shown above, find the length of side

Possible Answers:

14in

16in

13.5in

9in

5.5in

Correct answer:

16in

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides.

In this particular case the top sides that are connected at the top are congruent and the two sides that are connected at the bottom are congruent.

Thus, side must equal inches.

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Example Question #30 : Kites

A kite has one set of equivalent sides each with a measurement of 9.5 . Additionally, the kite has a perimeter of 26. Find the length for one of the other two sides of the kite.

Possible Answers:

5.5

9.5

3.5

Correct answer:

3.5

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula:

perimeter=2(a+b) , where and are the lengths of opposite sides of the kite and solve for .

26=2(9.5+b)

$9.5+b=\frac{26}{2}$

9.5+b=13

b=13-9.5=3.5

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Intermediate Geometry : Kites

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #21 : Kites

Example Question #22 : Kites

Example Question #23 : Kites

Example Question #21 : Kites

Example Question #21 : Kites

Example Question #26 : Kites

Example Question #27 : Kites

Example Question #28 : Kites

Example Question #29 : Kites

Example Question #30 : Kites

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