Question

The sides of a triangle are 7 cm,9cm& 14 cm. Its area is *​

Answer 1

Answer:

26.83 cm²

Step-by-step explanation:

According to the condition:-

Slide of the triangle= 7 cm

Base of the triangle= 9 cm

Side of the triangle= 14 cm

Let the slide be 'a', base be 'b' and side be 'c'

Using the formulas

A= √s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c /2

Solving for A

A=1/4√﹣a⁴+2(ab)²+2(ac)²﹣b⁴+2(bc)²﹣c⁴

=1/4·√﹣7⁴+2·(7·9)²+2·(7·14)²﹣9⁴+2·(9·14)²-14⁴

≈26.83282cm²

Answer 2

Given :

• 1st side of triangle is 7 cm
• 2nd side of triangle is 9 cm
• 3rd side of triangle is 14 cm

To find :

• Area of triangle

According to the question,

In this we will use Heron's formula,

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

$\implies \sf{s=\frac{7 + 9 + 14}{2} }$

$\sf \implies \sf{ s=\cancel\frac{30}{2} = 15 \: cm \orange \bigstar}$

$\implies\sf{ \sqrt{s(s - a)(s - b)(s - c)} }$

$\implies \sf{ \sqrt{15(15 - 7)(15 - 8)(15 - 14)} }$

$\implies \sf{ \sqrt{15(8)(6)(1)} }$

$\implies \sf{ \sqrt{3 \times 5 \times 2 \times 2 \times 2 \times 3 \times 2 \times 1} }$

$\implies \sf{2 \times 2 \times 3 \times \sqrt{5} }$

$\implies \sf{12 \sqrt{5} } \\ \implies \sf{12 \times 2.236}$

$\implies \sf{26.832} \: cm {}^{2} \orange \bigstar$

So,the area of triangle is 26.832 cm^2...