Question

if the sides of a triangle is 5 7 8 then its area

Answer 1

Step-by-step explanation:

If the sides of a Triangle are given and we need to find its area, then we use Heron's Formula.

What is the Heron's Formula?

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

Where s refers senior perimeter

Where a,b,c are the sides

Then use

$area= \sqrt{s(s - a)(s - b)(s - c)}$

So my semi perimeter is

$\frac{5 + 7 + 8}{2}$

My semi perimeter is 10.

Now,

s-a=10-5=5

s-b=10-7=3

s-c=10-8=2

So, my area will be

$area = \sqrt{10 \times 2 \times 3 \times 5}$

$area = \sqrt{300}$

$area = 17.32 \: {m}^{2}$

Answer 2

Answer:

10√3cm^2 ≈ 17.321cm^2

Step-by-step explanation:

Given Question :

The sides of a triangle is 5cm, 7cm, 8cm.

To find : it's area

Solution :

According to the heron's formula the area of triangle is

=√[ s(s-a)(s-b)(s-c) ]

Where 's' is the semi-perimeter

and 'a' , 'b' , 'c' are the three sides of a triangle.

Let 'a'=5cm

'b'=7cm

'c'=8cm

To find the semi perimeter of the triangle the formula is

s = (a+b+c)/2

By substituting the value of three sides of the triangle in the formula we get the semi perimeter as

s = (5+7+8)/2

s= (20)/2

s= 10cm

By substituting the value of semi perimeter and three sides in the heron's formula we get the area of the triangle as,

=√[ s(s-a)(s-b)(s-c) ]

=√[ 10(10-5)(10-7)(10-8) ]

=√[ 10×5×3×2]

=√300

=10√3cm^2

Ans : If the sides of a triangle is 5 7 8 then its area is 10√3cm^2 ≈ 17.321cm^2