Question

the sides of a triangle are 16 cm, 30 cm, 34 cm. its area is

a.225 cm²

b.225√3 cm²

c.225√2 cm²

d.400 cm²

​

Answer 1

Given:-

• 1st side of traingle (a) = 16 cm
• 2nd side of triangle (b) = 30 cm
• 3rd side of triangle (c) = 34 cm

To find:-

• The area of the triangle.

Solution:-

Here as we are given with the sides of a scalene triangle, we can find the area of the traingle using the Heron's Formula.

So let us first calculate the semi perimeter of the triangle,

We know,

✭ S = (a + b + c)/2

Hence,

S = (16 + 30 + 34)/2

=> S = 80/2

=> S = 40

Now,

Applying Heron's Formula,

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

Hence,

Area = √40(40 - 16) (40 - 30) (40 - 34)

Area = √40 × 24 × 10 × 6

Area = √2 × 2 × 2 × 5 × 2 × 2 × 2 × 3 × 2 × 5 × 2 × 3

Area = 2 × 2 × 2 × 2 × 3 × 5

Area = 240 cm²

Hence, Area of the triangle = 240 cm²

________________________________

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• 1st Side = 16 cm

• 2nd Side = 30 cm

• 3rd Side = 34 cm

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• The area of triangle

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

We know that ,

$\:\:$

➠ $\sf A = \sqrt { s(s - a)(s - b)(s - c) }$ ⚊⚊⚊⚊ ⓵

$\:\:$

Where ,

$\:\:$

• A = Area

• a = 1st side

• b = 2nd side

• c = 3rd side

• s = semi perimeter

• s = $\sf \dfrac { a + b + c } { 2 }$

$\:\:$

$\underline{\bold{\texttt{For the given triangle :}}}$

$\:\:$

• A = A

• a = 16

• b = 30

• c = 34

• $\sf s = \dfrac { 16 + 30 + 34} { 2 }$

• $\sf s = \dfrac { 80} { 2 } = 40$

$\:\:$

⟮ Putting the above values in ⓵ ⟯

$\:\:$

➜ $\sf A = \sqrt { s(s - a)(s - b)(s - c) }$

$\:\:$

➜ $\sf A = \sqrt { 40(40 - 16)(40 - 30)(40 - 34) }$

$\:\:$

➜ $\sf A = \sqrt { 40(24)(10)(6) }$

$\:\:$

➜ $\sf A = \sqrt { 400(24)(6) }$

$\:\:$

➜ $\sf A = \sqrt {20 \times 20 \times 2 \times 2 \times 2 \times 3 \times 2 \times 3}$

$\:\:$

➜ 20 × 2 × 2 × 3

$\:\:$

➜ 20 × 12

$\:\:$

➨ 240 sq. cm.

$\:\:$

• Hence the area of triangle is 240 sq. cm.