Question

hey guys! plz solve this fast...​

Answer 1

Answer:

Step-by-step explanation:

Hexagonal shaped Rangoli:

It can be observed that Hexagonal shaped Rangoli has 6 equilateral triangles in it.

Area of ΔOAB = √3/4 * Side² = √3/4 * (5)² = 25√3/4 cm².

Thus Area of hexagonal shaped rangoli = 6 * 25√3/4 = 150√3/4 cm².

Area of Equilateral triangle of side 1 cm = √3/4 * (1)² = √3/4 cm².

Thus number of equilateral triangles of side 1 cm that can be filled in the hexagonal shaped Rangoli =  150√3/4  / √3/4  = 150.

Star shaped Rangoli:

It can be observed that Star shaped Rangoli has 12 equilateral triangles in it.

Area of Star shaped Rangoli = 12 *√3/4*(5)² = 75√3.

Area of Equilateral triangle of side 1 cm = √3/4 * (1)² = √3/4 cm².

Thus number of equilateral triangles of side 1 cm that can be filled in the Star shaped Rangoli =  75√3 / √3/4  = 75*4 = 300.

Thus Star shaped rangoli has more equilateral triangles than Hexagonal shaped rangoli