# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.5 – Part 4

Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

Q-4 Complete the hexagonal rangoli and the star rangolies (See figure) but 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:

• In hexagonal, Number of equilateral triangles each of side 5 cm are 6.

• Area of equilateral triangle =

• Area of hexagonal =Area of an equilateral triangle rangoli

……………………..equation(1)

• Now area of equilateral triangle of side ………..equation(2)

• Number of equilateral triangles each of side 1cm in hexagonal rangoli

………………equation(3)

• Now in star

• Number of equilateral triangles each of side 5 cm=12

• Therefore , total area of star area of an equilateral triangle of side 5cm

……….equation(4)

• Number of equilateral triangles each of side 1 cm in star

……….equation (4)

• From eq. (3) and (4), we observe that star has more equilateral triangles each of side 1 cm.

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