Question

find the area of triangle when three sides of it is 10cm ,12cm,and 18cm​

Answer 1

Answer:8 root 5

Step-by-step explanation:

Let a = 10cm b= 12cm c = 18cm

Perimeter, p = 40

Semiperimeter, s = ( p/2) = 20

Using Heron's formula,

area of triangle = root of{(s)(s-a)(s-b)(s-c)}

= root{20 x 10 x 8 x 2}

= root{3200}

=root(2^7 x 5^2)

= 40 root 2 c$m^{2}$

Answer 2

$\huge \boxed{ \red{40 \sqrt{2} {cm}^{2} }}$

Step-by-step explanation:

Q.

Find the area of triangle when three sides of it is 10 cm, 12 cm and 18 cm.

.

Solution -

We can say that

side,

a = 10 cm

b = 12 cm

c = 18 cm

We have to find the semi-perimeter (s)

s = (a+b+c)/2

= (10+12+18)/2 cm

= 40/2 cm

= 20 cm

$area = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{20(20 - 10)(20 - 12)(20 - 18)} {cm}^{2} \\ \\ = \sqrt{20 \times 10 \times 8 \times 2} {cm}^{2} \\ \\ = \sqrt{10 \times 10 \times 2 \times 2 \times2 \times 2 \times 2} {cm}^{2} \\ \\ = \sqrt{ {10}^{2} \times {2}^{2} \times {2}^{2} \times 2} {cm}^{2} \\ \\ = 10 \times 2 \times 2 \sqrt{2} {cm}^{2} \\ \\ = 40 \sqrt{2} {cm}^{2}$

Hence area of the triangle = 40√2 cm²

hope it helps.