Question

find the area of triangle whose sides are 40cm,30cm,20cm

Answer 1

Use Heron’s formula,

S = 40+30+20/2

  = 90/2

  = 45.

Area = root of ( s(s-a)(s-b)(s-c) )                  where a,b,c are the sides

        = root of (45(45-40)(45-30)(45-20)

        = root of ( 45*5*15*25 )

        = root of 225*325

        = 15*18.02

Therefore Area ~ 270.41

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

∆PQR are the sides of triangle.

P = 20 cm

Q = 30 cm

R = 40 cm

Now,

Perimeter of ∆ = (P + Q + R)

= (20 + 30 + 40)

= 90

Semi perimeter

${\boxed{\sf\:{s=\dfrac{P+Q+R}{2}}}}$

$\tt{\rightarrow\dfrac{90}{2}}$

= 45 cm

Using Herons Formula

${\boxed{\sf\:{Area\;of\; \triangle=\sqrt{s(s-a)(s-b)(s-c)}}}}$

$\tt{\rightarrow\sqrt{45(45-20)(45-30)(45-40)}}$

$\tt{\rightarrow\sqrt{45\times 25\times 15\times 5}}$

$\tt{\rightarrow\sqrt{3^2\times 5\times 5^2\times 3\times 5\times 5}}$

$\tt{\rightarrow\sqrt{3^2\times 5^2\times 5^2\times 5\times 3}}$

$\tt{\rightarrow 3\times 5\times 5\sqrt{15}}$

$\tt{\rightarrow 75\sqrt{15}}$

= 75 × 3.8729

= 290.47 cm²