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
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.