Question

question :-

If the diagonals of a triangle are 19cm , 26cm and 21m respectively then find the area of a triangle by the heron's formula ?

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Answer 1

Correct Question :

If the sides of a triangle are 19cm , 26cm and 21m respectively then find the area of a triangle by the heron's formula ?

Before, finding the answer. Let's find out on how we find answer.

• First, we must find the semi-perimeter of triangle by the formula of :

$\sf \dfrac{a + b + c}{2}$

Here, a & b & c are the sides of triangle.

• Next, we must use the Heron's formula :

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

___________________

Given :

• Side A = 19 cm
• Side B = 26 cm
• Side C = 21 cm

To find :

• Area using Heron's formula

Solution :

$\sf Semi-perimeter = \dfrac{a+b+c}{2}$

$\sf = \dfrac{19+26+21}{2}$

$\sf = \dfrac{66}{2}$

$\sf = 33 cm$

Hence, the semi-perimeter is 33 cm.

$\sf Area \: by \: Herons \: Formula = \sqrt{s(s-a) (s-b)(s-c)}$

$\sf = \sf \sqrt{33(33-19) (33-26)(33-21)}$

$\sf = \sqrt{(33) \times (14) \times (7) \times (12) }$

$\sf = \sqrt{38808}$

$\sf = 42\sqrt{22}$

Hence, Area of the Triangle is 44√22.

Answer 2

$\huge{\underbrace{\textsf{\textbf{\color{lightpink}{Question:-}}}}}$

If the diagonals of a triangle are 19cm , 26cm and 21m respectively then find the area of a triangle by the heron's formula ?

$\underline{\underline{\huge{\gray{\tt{\textbf Solution:- }}}}}$

$\green{\underline\bold{For\: the \:given\: triangle,}}$

• a = 19cm
• b = 26cm
• c = 21cm

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

$\green{\underline\bold{To\: find:}}$

• Area of the triangle = ❓

${\large{\bold{\sf{\bf {\underline{Heron's\: Formula:}}}}}}$

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

Where,

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

S = $\frac{ 19+ 26+ 21}{2}$

S = 33

${\large{\bold{\sf{\bf {\underline{Applying \:heron's \: formula,\:we\:get:}}}}}}$

⇒A = $\displaystyle \sqrt{33(33-19)(33-26)(33-21)}$

⇒A = $\displaystyle \sqrt{33(14)(7)(12)}$

⇒A = $\displaystyle \sqrt{38808}$

⇒A = 196.99

$\pink{\underline\bold{∴ Area\: of\: the\: triangle\:= \:196.99.}}$

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