Question

Find area of equilateral triangle having height of 8√3

Answer 1

Answer:

64√3 cm²

Step-by-step explanation:

√3/2 × a = 8√3

√3 cancel on both sides

= a/2 = 8

a = 16 cm

Area of equilateral triangle = √3/4 a²

= √3/4 × 16 × 16

= 64√3 cm²

Answer 2

Answer:

64√3 cm²

Step-by-step explanation:

In ΔABC, AD is the height which is 8√3 cm.

We know that in an equilateral triangle all angles are 60°, and height, median and altitude bisect the base perpendicularly.

Consider ΔADC,

Tan C = AD/DC

Tan 60° = AD/DC

√3 = 8√3 / x         (Let DC be 'x')

x = 8√3 / √3

DC = x = 8 cm

DC + BD =8 + 8 = 16 cm

Area of equilateral triangle = √3/4 a²

= √3/4 × 16 × 16

= 64√3 cm²

Hence, area of equilateral triangle having height of 8√3 cm is 64√3 cm².