Question

find the area of the triangle whose sides are 150 cm 120 cm and 200 CM respectively ​

Answer 1

Step-by-step explanation:

Given :-

The sides of a triangle are 150 cm , 120 cm and 200 cm

To find :-

Find the area of the triangle ?

Solution :-

Given that

The three sides of the given triangle are 150 cm , 120 cm and 200 cm

Let a = 150 cm

Let b = 120 cm

Let c = 200 cm

We know that

Heron's formula ,

Area of a triangle (∆) = √[S(S-a)(S-b)(S-c)] sq.units

Where, S = (a+b+c)/2 units

Now,

S = (150+120+200)/2 cm

=> S = 470/2 cm

=> S = 235 cm

Now,

Area of the given triangle

=>∆=√[235(235-150)(235-120)(235-200)] sq.cm

=> ∆ = √(235×85×115×35) sq.cm

=> ∆ = √80399375 sq.cm

=> ∆ = 8966.57 sq.cm (approximately)

Therefore, Area = 8966.57 sq.cm

Answer :-

The area of the given triangle is

8966.57 sq.cm

Used formulae:-

Heron's formula:-

Let the sides of a triangle be a units , b units and c units then the area of the triangle

∆ = √[S(S-a)(S-b)(S-c)] sq.units

Where, S = (a+b+c)/2 units

Answer 2

Question:-

Find the area of a triangle whose sides are respectively 150cm, 120cm and 200cm.

Given:-

Sides:

• a = 150cm.
• b = 120cm.
• c = 200cm.

To Find:-

• Area of the triangle = ?.

Solution:-

Let, the perimeter of triangle be "S" Given that Sides of the triangles are 150cm, 120cm, and 200cm.

Semi - Perimeter:

${ \boxed{ \sf \large \red{S = \frac{(a + b + c)}{2} }}}$

$\sf \large S = \frac{(150 + 120 + 200)}{2}$

$\sf \large S ={{ \cancel{ \frac{470}{2} }}}$

${ \boxed{ \sf \large \red{S = 235cm.}}}$

Formula Used:-

By Using Heron's Formula:

${ \boxed{ \sf \large \blue{Area = s \sqrt{(s - a)(s - b)(s - c)} }}}$

$\sf \large Area = 235 \sqrt{(235 - 150)(235 - 120)(235 - 200)}$

$\sf \large Area = \sqrt{235 \times85 \times 115 \times 35}$

$\sf \large Area = \sqrt{80,399,375}$

$\sf \large Area = 8966.57cm {}^{2}.$

Answer:-

${ \boxed{ \sf \large \pink{∴ Area \: of \: the \: triangle = 8966.57cm {}^{2}. }}}$

Hope you have satisfied. ⚘