Question

Each side of an equilateral triangle measures 8 cm. Find

(i) the area of the triangle, correct to 2 places of decimal and

(ii) the height of the triangle, correct to 2 places of decimal. (Take √3 = 1.732)

Answer 1

(i) Consider a as the side of equilateral triangle i.e. a = 8cm

Area of an equilateral triangle = (√3 × a²)/4 sq units

So we get

Area of the equilateral triangle = (√3 × 8²)/4

On further calculation

Area of the equilateral triangle = (√3 × 64)/4

So we get

Area of the equilateral triangle = √3 × 16

By substituting the value of √3

Area of the equilateral triangle = 1.732 × 16 = 27.712

By correcting to two places of decimal

Area of the equilateral triangle = 27.71 cm²

(ii) We know that

Height of an equilateral triangle = √3/2 a

By substituting the value

Height of an equilateral triangle = √3/2 × 8

So we get

Height of an equilateral triangle = √3 × 4

By substituting the value of √3

Height of an equilateral triangle = 1.732 × 4 = 6.928

By correcting to two places of decimal

Height of an equilateral triangle = 6.93 cm