Question

an isscolated triangle has perimeter 30 cm and each equal sides is 12 cm . find the area of triangle​

Answer 1

Step-by-step explanation:

Let the third side be x cm

According to the problem,

x + 12 + 12 = 30

x + 24 = 30

x = 30 - 24

x = 6

Third side of the triangle = 6

Using Heron's Formula

Area of triangle = √s(s-a) (s-b) (s-c) sq. units

where s a + b + c / 2

s = 30/2 = 15

Area of triangle =

√15(15-12) (15-12) (15-6) cm²

= √15 multiply 3 multiply 3 multiply 9cm²

= 3 multiply 3 multiply √ 15cm²

9√15cm².

Answer 2

Answer:

Area of triangle = 9√(15) cm²

Step-by-step explanation:

Given:

• Perimeter = 30 cm

• Equal Sides are = 12 cm

To Find:

• Area of the triangle.

Formula used:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: area \: of \: triangle \: = \: \sqrt{s(s - a)(s - b)(s - c)}$

Procedue:

➝ Finding the unknown side of the triangle :

a = 12 cm

b = 12 cm

c = unknown

Given that equal sides are of 12 cm.

From the given information, we can infer that :-

→ a + b + c = 30 cm

→ 12 cm + 12 cm + c = 30 cm

→ 24 cm + c = 30 cm

→ c = 30 cm - 24 cm

→ c = 6 cm

➝ Finding area of triangle :

→ Semi perimeter = 30/2 = 15 cm

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: area \: of \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: area \: of \: triangle \: = \: \sqrt{15(15 - 12)(15 - 12)(15 - 6)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: area \: of \: triangle \: = \sqrt{15(3)(3)(9)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: area \: of \: triangle \: = \: \sqrt{15(3)(3)(3)(3)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: area \: of \: triangle \: = \sqrt{15 ({3}^{2}) ({3}^{2}) }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: area \: of \: triangle \: =9 \sqrt{15}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: area \: of \: triangle \: =9 \sqrt{15} \: \: {cm}^{2}$