Question

If the sides of a tringle are 8cm,9cm and 13cm ,find the area of the triangle​

Answer 1

☆ Solution ☆

Given :-

• Sides of triangle = 8cm, 9cm and 13cm

To Find :-

• Area of triangle

Step-by-Step-Explaination :-

As we know that herons formula :-

=> s = a + b + c / 2

=> s = 8 + 9 + 13 / 2

=> 30 / 2

=> 15

Thus,

Side = 15 cm

Now,

As we know that :-

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

Putting the respective value,

Area of triangle = √ 15 ( 15 - 8 ) ( 15 - 9 ) ( 15 - 13 )

Area of triangle = √ 15 × 7 × 6 × 2

Area of triangle = √ 1260

Area of triangle = 35.49 cm²

Hence,

Area of triangle = 35.49 cm²

Answer 2

Given :

⬤ Sides of Triangle are 8 cm , 9 cm and 13 cm .

To Find :

⬤ Area of Triangle .

Solution :

Let :

• Side a = 8 cm
• Side b = 9 cm
• Side c = 13 cm

As Per Question :-

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

$:\implies\sf{s=\dfrac{8+9+13}{2}}$

$:\implies\sf{\cancel\dfrac{30}{2}}$

$:\implies\bf{15}$

Now :

$:\implies\small\sf{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$:\implies\small\sf{Area=\sqrt{25(15-8)(15-9)(15-13)}}$

$:\implies\small\sf{Area=\sqrt{(15)\times{(7)}\times{(6)}\times{(2)}}}$

$:\implies\small\sf{Area=\sqrt{3\times{5}\times{7}\times{3}\times{2}\times{2}}}$

$:\implies\small\sf{3\times{2}\sqrt{7\times{5}}}$

$:\implies\bf{6\sqrt{35}\:{cm}^{2}}$

Therefore , The Area of Triangle is 6√35 cm² .