Question

find area of triangle sides are 14m,20m,18m by herons formula
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Answer 1

Answer:

• Area of triangle is 122.376 m².

Step-by-step explanation:

Given :-

• Sides of triangle are 14 m, 20 m and 18 m.

To find :-

• Area of triangle.

Solution :-

We know Heron's formula is :

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

Where,

• a, b and c are sides of triangle.
• s is semi-perimeter of triangle.

So,

Semi-Perimeter = Perimeter/2

$\rightarrow$ Semi-perimeter = 14 + 20 + 18/2

$\rightarrow$ Semi-perimeter = 53/2

$\rightarrow$ Semi-perimeter = 26

Semi-perimeter of triangle is 26 m.

Now,

$\longrightarrow$ Area = √26 × (26 - 14)(26 - 20)(26 - 18)

$\longrightarrow$ Area = √26 × 12 × 6 × 8

$\longrightarrow$ Area = √2 × 13 × 2 × 2 × 3 × 2 × 3 × 2 × 2 × 2

$\longrightarrow$ Area = 2 × 2 × 2 × 3 × √13 × 2

$\longrightarrow$ Area = 24 × √26

$\longrightarrow$ Area = 24 × 5.099

$\longrightarrow$ Area = 122.376

Therefore,

Area of triangle is 122.376 m².

Answer 2

Step-by-step explanation:

______________________________

$\text{\Large\underline{\red{Question:-}}}$

$\Longrightarrow$ ● Find the area of a triangle whose sides are 14m, 20m, and 18m by herons formula.

$\text{\Large\underline{\orange{To\ find:-}}}$

● In this question we have to find the area of the triangle .

$\text{\Large\underline{\green{Given:-}}}$

● Sides of the triangle is given by:- 14m, 20m, and 18m.

$\text{\large\underline{\blue{Formula\ to\ be\ used:-}}}$

$\bf\pink{●\ Area\ of\ triangle\ =\ \sqrt{s(s-a)(s-b)(s-c)}\ ●}$

$\text{\Large\underline{\purple{Solution:-}}}$

Here:-

● a, b, and c are the sides of the triangle.

● And s is for the semi-perimeter of the triangle.

The semi-perimeter of the triangle is not given. So, first we have to find the semi-perimeter of the triangle.

So:-

$\bf\pink{●\ Semi\ -\ perimeter\ =\ \dfrac{Perimeter}{2}\ ●}$

$\Longrightarrow$ $\sf{Semi\ -\ perimeter\ =\ 14\ +\ 20\ +\ \dfrac{18}{2}}$

$\Longrightarrow$ $\sf{Semi\ -\ perimeter\ =\ \dfrac{53}{2}}$

$\Longrightarrow$ $\sf{Semi\ -\ perimeter\ =\ 26.}$

Therefore:-

● Semi-perimeter of the triangle is 26m.

$\text{\large\underline{\green{According\ to\ the\ question:-}}}$

$\Longrightarrow$ $\sf{Area_{(triangle)}\ =\ \sqrt{26(26-14)(26-20)(26-18)}}$

$\Longrightarrow$ $\sf{Area_{(triangle)}\ =\ \sqrt{26×12×6×8}}$

$\Longrightarrow$ $\sf{Area_{(triangle)}\ =\ \sqrt{2×13×2×2×3×2×3×2×2×2}}$

$\Longrightarrow$ $\sf{Area_{(triangle)}\ =\ 2\ ×\ 2\ ×\ 2\ ×\ 3\ ×\ \sqrt{13×2}}$

$\Longrightarrow$ $\sf{Area_{(triangle)}\ =\ 24\ ×\ \sqrt{126}}$

$\Longrightarrow$ $\sf{Area_{(triangle)}\ =\ 24\ ×\ 5.099}$

$\Longrightarrow$ $\sf{Area_{(triangle)}\ =\ 122.376m².}$

$\Longrightarrow$ $\bf\purple{Area_{(triangle)}\ \approx\ 122.38m².}$

Hence:-

● The area of triangle is approximately 122.38m².

______________________________