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Answers
Answer:
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(i) From the figure, we can say that the rangoli is in the shape of a regular hexagon.
Let the area of hexagon be P
P=
2
3
3
(side)
2
=
2
3
3
×5
2
P=
2
75
3
cm
2
∴A(Rangoli)=
2
75
3
cm
2
Let area of equilateral triangle of side 1cm be A
′
A
′
=
4
3
(1)
2
=
4
3
cm
2
Let no. of equilateral triangles in rangoli be n
n=
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, the figure consist of 12 equilateral triangles each of side 5cm.
∴A(Rangoli)=12×
4
3
(5)
2
=75
3
cm
2
Let area of equilateral triangle of side 1cm be A
′
A
′
=
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.