Question

Herons formula:find the area of an equilateral triangle with side 10 cm

Answer 1

SoluTion:

Given that side of equilateral traingle is of 10 cm.

Therefore, a = b = c = 10 cm.

Semi perimeter = (10 + 10 + 10)/2

→ S = 30/2

→ S = 15 cm

Using heron's formula,

Ar ∆ABC = √{S(S-a)(S-b)(S-c)}

→ Ar ∆ABC = √{15(15-10)(15-10)(15-10)}

→ Ar ∆ABC = √(5 × 3 × 5 × 5 × 5)

→ Ar ∆ABC = √1875

→ Ar ∆ABC = 43.30 cm²

Hence, area will be 43.30 cm³

Answer 2

Given :-

• Side of equilateral triangle is 10 cm, it means all side of triangle is of 10 cm.

To find :- Area of triangle.

SolutioN:-

Height is not given , so we can't use 1/2 × base × height .

Therefore we use heron's formula that is:-

⎆ Area of triangle = $\sqrt{s(s - a)(s - b)(s - c)}$

So,

S = Perimeter /2

S = 10 + 10 + 10 /2

S = 30 /2

S = 15

Area of triangle =

$⇢\sqrt{15(15 - 10)(15 - 10)(15 -10)}$

$⇢ \sqrt{15 \times 5 \times 5 \times 5}$

$⇢ \sqrt{3 \times 5 \times 5 \times 5 \times 5}$

$⇢5 \times 5 \sqrt{3}$

$⇢25 \sqrt{3}$

$⇢25 \times 1.732$

$⇢43.3 cm² (approx)$

❝ Hence , Area of triangle is 43. 3 cm² (approx) ❞