(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 = 3√3/2(side)² = 3√3/2 × 5² P = 75√3/2 cm² ∴A(Rangoli) = 75√3/2 cm² Let area of equilateral triangle of side 1cm be A′ A′ = √3/4(1)² = √3/4 cm² Let no. of equilateral triangles in rangoli be n = A(Rangoli)/A(eq.Δof1cm) = (75√3/2)/(√3/4) = 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 consists of 12 equilateral triangles each of side 5cm. ∴A(Rangoli) = 12 × √3/4(5)² = 75√3 cm² Let area of equilateral triangle of side 1cm be A′ A′ = √3/4(1)² = √3/4 cm² No. of equilateral triangles in rangoli = A(Rangoli)/A(eq.Δof1cm) = 75√3/(√3/4) = 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.