Question

USING HERON'S FORMULA ONLY !!!!!!


The height of an equilateral triangle is 6cm. Find the area of the triangle

Take
$\ \textless \ br /\ \textgreater \ ( \sqrt{3 = } \: \: \: \: 1.732\ \textless \ br /\ \textgreater$

Using Heron's formula​​

Answer 1

Answer:

its height =√32*acm

side4√3

√34*48cm^2=12√3^2

hence the area of the given triangle is 12√3cm^2

Answer 2

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