Question

Find the area of a triangular field whose sides are 26m, 28m and 30m.​

Answer 1

Given:-

• Sides of the triangular fields are 26m,28m and 30m

To Find:-

• Find the area of the triangular field.

Concept:-

• Firstly let's go through the concept. Concept used here is Heron's Formula.

• Heron's formula gives the area of a triangle when the length of all three sides are known

• Unlike other triangle area formulae, there is no need to calculate angles or other distances in the triangle first.

Formulae Applied:-

• Area of the Triangle = √s(s - a)(s -b)(s - c)

Solution:-

Given that,

Sides of the triangular fields are 26m,28m and 30m

Area = ??

Firstly,

We have to find the Semiperimeter

Semiperimeter = perimeter/2

S = p/2

= perimeter/2

= 26 + 28 + 30/2

= 42

= 42m

Hence,

The Semiperimeter is 42m.

Now,

Area of the Triangle = √s(s - a)(s -b)(s - c)

= √s(s - a)(s -b)(s - c)

= √42(42 - 26)(42 - 28)(42 - 30)

= √42 (16) (14) (12)

= √42 × 16 × 14 × 12

= √112896

= 336

= 336m

Hence,

The area of the triangle is 336m.

Answer 2

$\bf\bigstar{QUESTION:-}$

Find the area of a triangular field whose sides are 26m, 28m and 30m.​

$\bf\bigstar{ANSWER:-}$

   $\bf\bullet$   Sides of the triangle are given : 26 m , 28 m & 30 m.

   $\bf\bullet$    We need to find it's area !

   $\bf\bullet$     As we know, area of triangle can be find by using Heron's formula.

$\huge{\boxed{\bf{Heron's \: formula=\sqrt{{s} (s-a)(s-b)(s-c)}}}}}}$

  $\bf\bullet$   This is the required formula we need to apply here.

   $\bf\bullet$ S here means the semiperimeter.

   $\bf\bullet$ Perimeter = ( 26 + 28 + 30 ) m = 84 m

   $\bf\bullet$ So, S = 84 / 2 = 42 m.

 Now we can apply the formula here,

 ie, area of the triangle =  √s(s - a)(s -b)(s - c)

⇒ √42(42 - 26)(42 - 28)(42 - 30)  m²

⇒ √42 (16) (14) (12)  m²

⇒ √42 × 16 × 14 × 12  m²

⇒ √112896  m²

⇒ 336  m²

Hence the area of the triangle is 336 m².

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