Question

Find the area of the triangle whose side are 21 cm, 20 cm, 13 cm used heron's formula
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Answer 1

To find:-

• The area of triangle .

Answer:-

The given sides of triangle are 21cm , 20cm and 13cm . For a traingle of sides
`a` ,
`b` and
`c` , area of triangle by Heron's Formula is given by,

`\implies A =√( s(s-a)(s-b)(s-c)) \\`

where,

• s is semi perimeter.

We can find semi perimeter as ,

`\implies s =(a+b+c)/(2) \\`

`\implies s =(21cm + 20cm + 13cm)/(2) \\`

`\implies s =(54)/(2)=\boxed{27}`

Now on substituting the respective values, we have;

`\implies A =√( 27 ( 27 - 21) (27-20)(27-13))cm^2 \\`

`\implies A =√( 27 \ . \ 6 \ . \ 7 \ . \ 14)cm^2\\`

`\implies A =√( 3^3 \ . \ 3 \ . \ 2 \ . \ 7 \ . \ 7 \ . \ 2) cm^2\\`

`\implies A = 3^2 \ . \ 2 \ . \ 7 cm^2 \\`

`\implies Area = 126 cm^2 \\`

Hence the area of the traingle is 126 cm² .

and we are done!

Answer 2

126cm².

Explanation:

To use Heron's formula to find the area (A) of a triangle given the lengths of its sides, we need to first calculate the semiperimeter (s), which is half the perimeter of the triangle:

s = (21 + 20 + 13) / 2 = 27

Then, we can use the formula:

A = sqrt(s(s-a)(s-b)(s-c))

where a, b, and c are the lengths of the sides of the triangle. Substituting the values, we get:

A = sqrt(27(27-21)(27-20)(27-13))

A = sqrt(27 x 6 x 7 x 14)

A = sqrt(15876)guu

A=126 cm²

Therefore, the area of the triangle is approximately 126cm².