maths work book

MATHEMATICS WORK BOOK

POLYGONS

GENERAL OBJECTIVES

1 To understand about polygons.2 To identifies different types of polygons.3 To understand sum of angles of a polygon having n- sides is equal to (n-2)180°.4 To apply the above formula to solve the

problems.5 To understand the sum of exterior angles of an n-

sided polygon.6 To apply the formula for solving problems.7 To understand about regular polygons.

ACTIVITY 1Filling the blanks

1. A closed figure of 3 sides and angles is called a …………

2. A closed figure of 4 sides and angles is known as a ………

3. A Heptagon is a closed figure of …… Sides and angles.4. A closed figure of five sides and angles is called a

…………5. A closed figure with 3 or more sides is known as a

…………6. An octagon is a closed shape of ………Sides and angles.

Name :Date :

ACTIVITY 2 1) Complete the table

Name of the polygon

Splitted figure

Number of triangles

Sum of the interior angles

TRIANGLE

……A……… …B…………

QUADRILATERAL

………C…… …………D…

Name of the polygon

Splitted figure

Number of triangles

Sum of the interior angles

PENTAGON

……E……… …F…………

HEXAGON

……G……… ………H……

HEPTAGON

……I……… ……J………

2) What is the sum of angles of a 10–sided polygon ?

The sum of angles of a 10–sided polygon is …………

3) The sum of angles of a 15-sided polygon is ……………

4) If we draw maximum possible diagonals from a vertex of an n-sided polygon then how many triangles we get ?

ans : ……………

5) What is the sum of angles of an n- sided polygon ? ans : ……………

2) What is the sum of angles of a 10–sided polygon ?

The sum of angles of a 10–sided polygon is …………

3) The sum of angles of a 15-sided polygon is ……………

4) If we draw maximum possible diagonals from a vertex of an n-sided polygon then how many triangles we get ?

ans : ……………

5) What is the sum of angles of an n- sided polygon ? ans : ……………

ACTIVITY 31.The following are the number of sides of a polygon. Find the sum of the angles of each polygon

a) n=12 Sum of the angles of a 12 sided polygon= …………

b) n=15Sum of the angles of a 15 sided polygon= …………

c) n=20Sum of the angles of a 20 sided polygon= …………

d) n=24Sum of the angles of a 24 sided polygon= …………

2 . The sum of the angles of a polygon is 2700° . How many sides does it have ?

The sum of the angles of a polygon is ……………Given,

The sum of the angles of a polygon is ……… That is, ………………………………………….. Therefore n= …………..

3. The sum of the angles of polygons are given below. Find the number of sides of each polygons.

a) 900°The sum of the angles of a polygon is ……………Given,

The sum of the angles of a polygon is ……… That is, ………………………………………….. Therefore n= …………..

b)1260°The sum of the angles of a polygon is ……………Given,

The sum of the angles of a polygon is ……… That is, ………………………………………….. Therefore n= …………..

c)1980°The sum of the angles of a polygon is ……………Given,

The sum of the angles of a polygon is ……… That is, ………………………………………….. Therefore n= …………..

d)2520° The sum of the angles of a polygon is ……………Given,

The sum of the angles of a polygon is ……… That is, ………………………………………….. Therefore n= …………..

ACTIVITY 41) The angles of a triangle are 30°,40°, and 110°

i) Find the measures of its external angles (a),(b), (c)and give reasons?

External angle (a)= ………….. (Since ……………. )External angle (b)= ………….. (Since ……………. )External angle (c)= ………….. (Since ……………. )

ii) Find the sum of external angles?

sum of external angles = ……………

30 °

110°

40 ° a)

b)

c)

2) Look at the figure and answer the questions.

i. Name the polygon?

………………… ii. What is the sum of angles of this polygon ? …………………

iii. Find the external angles (a),(b),(c) &(d) and give reasons.External angle (a)= ………….. (Since ……………. )External angle (b)= ………….. (Since ……………. )External angle (c)= ………….. (Since ……………. )External angle (d)= ………….. (Since ……………. )

iv . Find the sum of these external angles ?

sum of external angles = ……………

35 ° 50 °

155 °120 °

a)

b)

c)

d)

3) Answer the following

i) A pentagon have ……… sides. ii) Find all the external angles (a),(b),(c),(d) & (e)

External angle (a)= ………….. (Since ……………. )External angle (b)= ………….. (Since ……………. )External angle (c)= ………….. (Since ……………. )External angle (d)= ………….. (Since ……………. )

External angle (e)= ………….. (Since ……………. )

iii)Find sum of the external angles of these pentagon ?

Sum of external angles = ……………

)30◦160◦

72◦

70 ◦108 ◦ a)

b)c)

d)

e)

4) Answer the following

i. How many external angles in these hexagon?…………….

ii. Find all external angles ?

External angle (a)= ………….. (Since ……………. )External angle (b)= ………….. (Since ……………. )External angle (c)= ………….. (Since ……………. )External angle (d)= ………….. (Since ……………. )External angle (d)= ………….. (Since ……………. )

iii. Find the sum of these external angles ?

Sum of external angles = ……………

5)What is the sum of the external angles of an n-sided polygon?……………………

120 ◦ 120◦120 ◦

120 ◦120 ◦120 ◦

a)

b)

c)

d)

e)f)

ACTIVITY 51) If all angles of a triangle are equal .Then sides of the triangle

are also …………………2) If the angles of a quadrilateral are all equal , is it necessary

that its sides are also equal ? ………………3) Define a regular polygon and name a 5 sided regular polygon.

A regular polygon is a ……………………………………

4) How much is each angle of a regular hexagon ?Sum of the interior angle of a hexagon=

………………one angle of a regular

hexagon=…………………………5) Find each angle of a regular octagon?

Sum of the interior angle of an octagon= ………………

one angle of a regular octagon=…………………………

ACTIVITY 61) An external angle of a regular polygon is 45° ,find number of sides

of the regular polygonGiven,External angle = …………Sum of the external angles of a polygon = …………Number of external angles= ……………Therefore number of sides =……………

2) If the external angles of a triangle are (2x+30°) ,(3x−10°) &100° then find the value of x ?

Since sum of the external angles of a triangle is …………

we can write 2x+30+3x−10+100 = ………………………

……………………..

…………………….

x= …………………

<A=…………

ABC is an isosceles triangle(since <B=……… , Also AB=BC ,the two angles are equal ).

Therefore <BAC=………… Similarly, From ADE, <EAD=………

Therefore <CAD= …………

Sum of the angles of a regular pentagon=……………

Therefore ,one angle of the regular pentagon=…………

3) ABCDE is a regular polygon. Find <CAD ?A

B

C D

E

4) ABCDEF is a regular hexagon . Prove ACE is an equilateral triangle.

sum of the angles of a regular hexagon =…………… Therefore ,one angle of the regular hexagon=………… ie, <A = ………

From the isosceles triangle AEF , <F=………… Also the two angles are equal, therefore <FAE=………Similarly, From ABC, <BAC=……… Therefore, <EAC=………Similarly we have <ACE=……… So we can prove <AEC=………Therefore ACE is an equilateral triangle.

A B

C

DE

F

5) Draw a hexagon with all angles equal but not all sides equal ?

6) One of the external angle of a regular polygon is 23° is it possible ? why?

ANSWERSACTIVITY 11) Triangle2) Quadrilateral3) 7 sides and angles4) Pentagon5) Polygon6) 8 sides and angles

ACTIVITY 21) A=1 ,B=180° C=2 ,D=2*180° E=3 ,F=3*180° G=4 ,H=4*180° I=5 ,J= 4*180°2)1440°3)2340 °4) (n-2)5) (n-2)180 °

ACTIVITY 31) a)=1800 °,b)=2340 °,c)=3240 °,d)=3960 °2) n=173) a) n=7

b) n=9c) n=13d)n= 16

ACTIVITY 41) i) a)=150 ° ,b)=70 ° ,c)=140 ° { since linear pairs} ii) 360°2) i) Quadrilateral ii) 360° iii) i) a)=145 ° ,b)=60 ° ,c)=25 ° ,d=130 ° { since

linear pairs} iv) 360°3) i) 5 sides ii) i) a)=110 ° ,b)=108 ° ,c)=20 ° ,d=150 ° ,e=72 ° iii) 360°

ACTIVITY 44) i) 6 ii) All angles are 60 ° iii) 360 °5) 360 °

ACTIVITY 51) Equal2) No3) A polygon with equal angles and lengths of

sides also equal are called regular polygon.4) 120 °5) 135 °

ACTIVITY 61) No. of sides= 82) x=483) Sum of the angles of a regular pentagon= 540 °

Therefore ,one angle of the regular pentagon= 540/5=108 ° <A=108 °

ABC is an isosceles triangle(since <B=108 ° , Also AB=BC ,the two angles are equal ).

Therefore <BAC=36 ° Similarly, From ADE, <EAD= 36 °

Therefore <CAD= 108-(36+36)=36 °

4) sum of the angles of a regular hexagon =720 ° Therefore ,one angle of the regular hexagon=720/6=120 ° ie, <A = 120 °

From the isosceles triangle AEF , <F=120 ° Also the two angles are equal, therefore <FAE= <FAESimilarly, From ABC, <BAC=30 °Therefore, <EAC=120-(30+30)=60 °Similarly we have <ACE=60 °So we can prove <AEC= 60 ° Therefore ACE is an equilateral triangle.

5) From the point A draw a line by making an angle 120 ° .In any length mark F on that line. Similarly draw a line and mark C. Then draw a parallel line corresponding to AF through C. And mark D on that line ,draw a parallel line corresponding to BC through F, measure 120 ° from the point D.

6) No Since no .of external angles = no. of sides Therefore no. of external angles =360/23= not an integer value. so 23 ° is not an exterior angle of a regular polygon.

Prepared by,VINYA.P

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