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?
![Complete the hexagonal and star shaped rangolies s [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?](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/15-1569577501.png)
Solution:
It can be observed that hexagonal-shaped rangoli has 6 equilateral triangles of side 5 cm in it.
![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?](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/20-1568810994.png)
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.
![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?](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/4-3-1567577015.png)
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.
☛ Check: NCERT Solutions Class 9 Maths Chapter 7
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.
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