# 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?

**Solution:**

It can be observed that hexagonal-shaped rangoli has 6 equilateral triangles of side 5 cm in it.

Lets find the area of Δ OAB

Area of an equilateral triangle of side 'a' is given by √3/4 a²

Area of ΔOAB = √3/4 (side)²

= √3/4 (5 cm)²

= (25√3)/4 cm²

Area of hexagonal-shaped rangoli = 6 × (25√3)/4 cm² = (75√3)/2 cm²

Area of an equilateral triangle of side 1 cm = √3/4 (1 cm)² = √3/4 cm²

Number of equilateral triangles of 1 cm side that can be filled in this hexagonal-shaped Rangoli = Area of hexagonal-shaped rangoli / Area of an equilateral triangle of side 1 cm

⇒ (75√3)/2 / √3/4 = 150

Star-shaped rangoli has 12 equilateral triangles of side 5 cm in it.

Area of star-shaped rangoli

= 12 × √3/4 × (5)²

= 75√3

Number of equilateral triangles of 1 cm side that can be filled in this star-shaped rangoli = Area of star-shaped rangoli / Area of an equilateral triangle of side 1 cm

= (75√3) / √3/4

= 300

Therefore, star-shaped rangoli has more number of equilateral triangles in it.

**Video Solution:**

## Complete the hexagonal and star shaped rangolies (see the given figures) 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?

### NCERT Maths Solutions Class 9 - Chapter 7 Exercise 7.5 Question 4:

**Summary:**

The number of equilateral triangles of 1 cm side that can be filled in the hexagonal-shaped Rangoli and the star-shaped rangoli are 150 and 300 respectively. Star-shaped rangoli have more number of equilateral triangles.