Math, asked by manojpandit1171973, 9 months ago

Complete the hexagonal and star shaped Rangolies (see Fig. 7.53 (i) and (ii)] by filling
them with as many equilateral triangles of side 1 cm as you can. Count the number of
triangles in each case. Which has more triangles?

Answers

Answered by satapathysmruti01
12

ANSWER

(i) From the figure, we can say that the rangoli is in the shape of a regular hexagon.

Hence, 6 equilateral triangles each of side 5cm, can be drawn in it.

A(ΔPQR)=

4

3

(side)

2

=

4

3

×5

2

A(ΔPQR)=

4

25

3

cm

2

∴A(Rangoli)=6×A(ΔPQR)=

4

150

3

cm

2

Area of equilateral triangle of side 1cm=

4

3

(1)

2

=

4

3

cm

2

No. of equilateral triangles in rangoli=

A(eq.Δof1cm)

A(Rangoli)

=

4

3

4

150

3

=150

There can be 150 equilateral triangles each of side 1cm in the hexagonal rangoli.

(ii) From the figure, we can say that the rangoli is in the shape of a star.

Hence, 12 equilateral triangles each of side 5cm, can be drawn in it.

∴A(Rangoli)=12×

4

3

(5)

2

=75

3

cm

2

Area of equilateral triangle of side 1cm=

4

3

(1)

2

=

4

3

cm

2

No. of equilateral triangles in rangoli=

A(eq.Δof1cm)

A(Rangoli)

=

4

3

75

3

=300

There can be 300 equilateral triangles each of side 1cm in the hexagonal rangoli.

Hence, star shaped rangoli has more equilateral triangles in it.

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