Question

the height of an equilateral triangle is 6 cm. find its area (using heron's 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:

it's height, =√32*a

side4√3

√34*48cm2=12√3cm^2

han Stadium area of triangle is it 12√ 3 cm^2