Bu'aan kutaa 12ffaa ba'eera; bu'aa kee eessatti akka ilaaltu

Yaadannoo boqonnaa fi gaaffii shaakalaa

Boqonnaa 6 Herrega kutaa 9: Pooliigoonoota Idilee

Wanti fuula kana irra jiru hundi boqonnaa 6 kitaaba Herrega kutaa 9 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.

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3
Kaardii
10
Gaaffii shaakalaa boqonnaa 6
181–208
Fuula kitaabaa boqonnaa 6

Boqonnaan 6 maal haguuga

  1. 1.Sum of Interior Angles of a Convex Polygon
  2. 2.Sum of Exterior Angles of a Convex Polygon
  3. 3.Measures of Each Interior Angle and Exterior Angle of a Regular Polygon
  4. 4.Properties of Regular Polygons: pentagon, hexagon, octagon and decagon

Yaadannoo gabaabaa boqonnaa 6

Kaardiiwwan fuula Herrega kutaa 9 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.

A=12aPA = \frac{1}{2} a P
AA
bal'ina rog-baay'ee qajeelaam2\text{m}^2
aa
apoozemii rog-baay'ee qajeelaam\text{m}
PP
naannawa rog-baay'ee qajeelaam\text{m}

Yoom akka itti fayyadamtu

Apothem fi perimeter tolfagee idilee yeroo beekamanitti bal'ina isaa shallaguuf foormulaa kanatti fayyadamaa.

Of eeggadhu

Apothem jechuun fageenya qajeelaa giddu-galeessa irraa gara cinaachaatti jiru dha malee raadiyeesii gara koflaatti jiru miti.

Grade 9 Mathematics, fuula 181-208 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

θ=(n−2)×180∘n\theta = \frac{(n - 2) \times 180^\circ}{n}
θ\theta
safara kofa keessoo tokkoon tokkoo∘^\circ
nn
baay'ina cinaachota rog-baay'ee qajeelaa11

Yoom akka itti fayyadamtu

Hangi kofla keessoo tokkoo tolfagee idilee hunda kofloota walqixa qabu keessatti shallaguuf itti fayyadamaa.

Of eeggadhu

Foormulaan kun tolfagee idileef qofa hojjeta. Tolfageen idilee hin taane kofloota walqixa hin qabu.

Grade 9 Mathematics, fuula 181-208 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

s=2rsin⁡(180∘n)s = 2r \sin\left(\frac{180^\circ}{n}\right)
ss
dheerina cinaacha rog-baay'ee qajeelaam\text{m}
rr
raadiyeesii geengoo naannoom\text{m}
nn
baay'ina cinaachota rog-baay'ee qajeelaa11

Yoom akka itti fayyadamtu

Tolfagee idilee cinaacha n qabu kan geengoo raadiyeesii r keessatti sarqameef dheerina cinaachaa shallaguuf itti fayyadamaa.

Of eeggadhu

Sararri qajeelaan cinaacha bakka lamatti waan qooduuf 2n baay'isuu hin dagatinaa.

Grade 9 Mathematics, fuula 181-208 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Gaaffii shaakalaa boqonnaa 6

Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.

Gaaffii 1

According to the definition, what is a regular polygon?

  1. A.A polygon that is equiangular (equal angles) and equilateral (equal sides)
  2. B.A polygon with at least one interior angle greater than 180 degrees
  3. C.Any closed plane figure with four unequal sides
  4. D.A polygon whose vertices point inwards
Deebii fi sababa agarsiisi

Deebii: A A polygon that is equiangular (equal angles) and equilateral (equal sides)

Sababa

A polygon is regular if it is both equiangular (all interior angles are equal) and equilateral (all sides are equal in length).

Gaaffii 2

How many lines of symmetry does an n-sided regular polygon have?

  1. A.n - 2
  2. B.n
  3. C.2n
  4. D.n / 2
Deebii fi sababa agarsiisi

Deebii: B n

Sababa

An n-sided regular polygon always has exactly n lines of symmetry. For example, a regular hexagon (6 sides) has 6 lines of symmetry.

Gaaffii 3

What is the sum of the measures of the exterior angles of any convex polygon?

  1. A.180°
  2. B.360°
  3. C.540°
  4. D.720°
Deebii fi sababa agarsiisi

Deebii: B 360°

Sababa

For any n-sided convex polygon, the sum of the measures of the exterior angles is always 360°.

Gaaffii 4

What is the measure of each exterior angle of a regular pentagon (5-sided polygon)?

  1. A.60°
  2. B.72°
  3. C.108°
  4. D.120°
Deebii fi sababa agarsiisi

Deebii: B 72°

Sababa

The measure of each exterior angle of an n-sided regular polygon is 360° / n. For a pentagon with n = 5, the measure is 360° / 5 = 72°.

Gaaffii 5

What is the sum of the interior angles of a convex heptagon (a 7-sided polygon)?

  1. A.720°
  2. B.900°
  3. C.1,080°
  4. D.1,260°
Deebii fi sababa agarsiisi

Deebii: B 900°

Sababa

The sum of the interior angles of an n-sided polygon is (n - 2) × 180°. For a heptagon, n = 7: (7 - 2) × 180° = 5 × 180° = 900°.

Gaaffii 6

A student in Hawassa finds that the sum of the interior angles of a polygon is 1,440°. How many sides does the polygon have?

  1. A.8
  2. B.9
  3. C.10
  4. D.12
Deebii fi sababa agarsiisi

Deebii: C 10

Sababa

Using the formula (n - 2) × 180° = 1,440°, we divide both sides by 180° to get n - 2 = 8, which gives n = 10 (a decagon).

Gaaffii 7

What is the measure of each interior angle of a regular octagon (8-sided polygon)?

  1. A.108°
  2. B.120°
  3. C.135°
  4. D.144°
Deebii fi sababa agarsiisi

Deebii: C 135°

Sababa

Each interior angle of an n-sided regular polygon is ((n - 2) × 180°) / n. For an octagon (n = 8), this is ((8 - 2) × 180°) / 8 = 1,080° / 8 = 135°.

Gaaffii 8

What is the measure of each central angle of a regular decagon (10-sided polygon)?

  1. A.36°
  2. B.45°
  3. C.60°
  4. D.72°
Deebii fi sababa agarsiisi

Deebii: A 36°

Sababa

The measure of each central angle of an n-sided regular polygon is 360° / n. For a decagon, n = 10, so 360° / 10 = 36°.

Gaaffii 9

Four interior angles of a pentagon measure 95°, 100°, 120°, and 70°. What is the measure of the fifth interior angle?

  1. A.135°
  2. B.145°
  3. C.155°
  4. D.165°
Deebii fi sababa agarsiisi

Deebii: C 155°

Sababa

The sum of the interior angles of a pentagon is (5 - 2) × 180° = 540°. The sum of the four given angles is 95° + 100° + 120° + 70° = 385°. The fifth angle is 540° - 385° = 155°.

Gaaffii 10

A square is inscribed in a circle of radius r = 5 cm. Using the formula s = 2r sin(180° / n), what is the side length s of the square?

  1. A.5 cm
  2. B.5√2 cm
  3. C.10 cm
  4. D.10√2 cm
Deebii fi sababa agarsiisi

Deebii: B 5√2 cm

Sababa

For a square, n = 4. Side length s = 2(5) sin(180° / 4) = 10 sin(45°) = 10 × (1 / √2) = 5√2 cm.

Appiin boqonnaa kana irratti gaaffii 12 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.

Viidiyoo barnootaa boqonnaa 6

Barnoota boqonnaa kanaa YouTube irraa. Yommuu play tuqxu qofa fe'ama.

Sum of the exterior angles of convex polygon · YouTube irratti ilaali

Barnoota dabalataa boqonnaa kana irratti

Fuula kitaabaa boqonnaa 6

Boqonnaan 6 Maxxansa Ministeera Barnootaa keessatti fuula 181 hanga fuula 208 ti.

Maxxansa Ministeera Barnootaa, Ingiliffaa, Fuula 337

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