Question

one side of an equilateral triangle measure 8 cm . find it's area using heron's formula. what is its altitude​

Answer 1

Answer:

area = 16√3

altitude = 4√3

Step-by-step explanation:

herons formula

area = √s(s-a)(s-b)(s-c)

s = (a+b+c)/2

s = (8+8+8)/2 = 24/2 = 12

$= \sqrt{12(12 - 8)(12 - 8)(12 - 8)} \\ = \sqrt{12 \times 4 \times 4\times 4 } \\ = \sqrt{3 \times 4 \times 4 \times 4 \times 4} \\ = 4 \times 4 \times \sqrt{3} \\ = 16 \sqrt{3}$

area of equilateral triangle = 16√3

$\frac{1}{2} \times b \times h = 16 \sqrt{3} \\ \frac{1}{2} \times 8 \times h = 16 \sqrt{3} \\ 4h = 16 \sqrt{3} \\ h = \frac{16 \sqrt{3} }{4} \\ h = 4 \sqrt{3}$