Question

Find the area of a triangle where sides are 10 cm 24 ,cm and 26 cm using Herons formula​

Answer 1

Answer:

120cm^2

Step-by-step explanation:

So the herons formula is:

s=(a+b+c)/2

Ar= √s*(s-a)*(s-b)*(s-c)

let's calculate now:

s= 10+24+26/2= 60/2=30

Ar=√30*30-24*30-26*30-10

=√30*6*4*20

=√3*2*5*3*2*2*2*2*2*5

=3*5*2*2*2

=15*8

=120 cms²

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Answer 2

Given :

A triangle whose sides are 10 cm 24 ,cm and 26 cm.

To Find :

The area of triangle.

Solution :

Analysis :

Here we have to first find the perimeter of the triangle and then from the perimeter we can get the semiperimeter and then use the Heron's Formula to find the area of the triangle.

Required Formula :

• Perimeter = a + b + c

• Area = √[s(s - a)(s - b)(s - c)]

where,

• a = First side
• b = Second side
• c = Third side
• s = Semiperimeter

Explanation :

We know that the three sides of a triangle add upto its perimeter.

☯ According to the question,

⇒ Perimeter = a + b + c

where,

• a = 10 cm
• b = 24 cm
• c = 26 cm

Substituting the values,

⇒ Perimeter = 10 + 24 + 26

⇒ Perimeter = 40 cm

∴ Perimeter = 60 cm.

Now the Area :

First we have to find the semiperimeter.

Semiperimeter = Perimeter/2

where,

• Perimeter = 60 cm

Substituting the values,

⇒ Semiperimeter = Perimeter/2

⇒ Semiperimeter = 60/2

⇒ Semiperimeter = 30

∴ Semiperimeter = 30 cm.

We know that if are given the three sides of the triangle and the semiperimeter and is asked to find the area then the Heron's Formula is,

Area = √[s(s - a)(s - b)(s - c)]

where,

• s = 30 cm
• a = 10 cm
• b = 24 cm
• c = 26 cm

Using the required formula and substituting the required values,

⇒ Area = √[s(s - a)(s - b)(s - c)]

⇒ Area = √[30(30 - 10)(30 - 24)(30 - 26)]

⇒ Area = √[30(20)(6)(4)]

⇒ Area = √[30 × 20 × 6 × 4]

⇒ Area = √[14400]

We know that 120 × 120 = 14400,

⇒ Area = √[120 × 120]

⇒ Area = 120

∴ Area = 120 cm².

Area of the triangle is 120 cm².