Question

The height of equilateral triangle is 6cm find the area of triangle with herons formula?

Answer 1

Hii friend,

Height of an equilateral triangle = 6 cm

✓3/2 × Side = 6

Side = 6×2/✓3

Side = 12/✓3 × ✓3/✓3 = 12✓3/3 = 4✓3 cm

Length of each side of an equilateral∆ = 4✓3 cm.

S = 1/2× (side+Side+Side)

S = 1/2 × (3×4✓3)

S = 1/2 × 12✓3 = 6✓3 cm

Therefore,

(S-a) = (6✓3 - 4✓3) = 2✓3

(S-b) = (6✓3 - 4✓3) = 2✓3

(S-c) = (6✓3 - 4✓3) = 2✓3

So , by herons formula, we have:

Area = ✓S(S-a)(S-b)(S-c) cm²

= ✓6✓3(2✓3)(2✓3)(2✓3)

= ✓6✓3 × 8 × 3✓3

=> ✓6✓3 × 24✓3 = ✓144 × 3

=> ✓432 = 20.78 cm²

Hence,

The area of an equilateral triangle is 20.78 cm²


HOPE IT WILL HELP YOU....... :-)

Answer 2

Answer:

Area = $9\sqrt{3}$

Step-by-step explanation:

Area = $\sqrt{3} a^{2}/4$

        = root 3 * 6^2

        = $9\sqrt{3}$