Question

find the area of an isosceles triangle with two equal sides are 5 cm each and the third side as 8 cm (using heron's formula)​

Answer 1

Answer:

• Area of triangle = 12 cm²

Step-by-step explanation:

Given:

• Two equal sides of isosceles triangle = 5 cm
• Third side = 8 cm.

To Find:

• Area of isosceles triangle by Heron's Formula.

$\underline{\bf Now,\;we\;know\;that,}\\ \\ \\ \implies \sf s = \dfrac{a+b+c}{2}\\ \\ \bf Where,\;a=5,\;b=5,\;and\;c=8. \\ \\ \\ \implies \sf s=\dfrac{5+5+8}{2}\\ \\ \\ \implies \sf s=\dfrac{18}{2}\\ \\ \\ \implies \sf s = 9 \\ \\ \rule{100}{2}\\ \\ \implies \sf Area\;of\;triangle=\sqrt{s(s-a)(s-b)(s-c)} \\ \\ \\ \implies \sf Area\;of\;triangle=\sqrt{9(9-5)(9-5)(9-8)}\\ \\ \\ \implies \sf Area\;of\;triangle=\sqrt{9\times 4 \times 4\times 1}\\ \\ \\ \implies \sf Area\;of\;triangle=\sqrt{144}$

$\implies \sf Area\;of\;triangle=12\;cm^{2}\\ \\ \\ \underline {\bf Hence\;Area\;of\;Triangle=12\;cm^{2}}$

Answer 2

AnswEr:-

Area of isosceles triangle = 12 cm²

$\rule{200}{1}$

Given :-

• Equal sides = 5 cm each
• Inequal side = 8 cm

To find :-

• Area of isosceles triangle = ?[Using Heron's formula]

As we know,Heron's formula:-

$\star\:\large\blue{\boxed{\rm{\blue{Area_{triangle} = \sqrt{s(s - a)(s - b)(s - c)} }}}}$

Here,a = one equal side,b = another equal side & c = inequal side.

And,s = Semi-perimeter of triangle.

Now,

↠ Semi-perimeter = Perimeter/2

↠ Semi-perimeter = (8 + 5 + 5)/2

↠ Semi-perimeter = 18/2

↠ Semi-perimeter = 9 cm

According to question:-

$\dashrightarrow\sf Area\: of \: triangle = \sqrt{9(9 - 5)(9 - 5)(9 - 8)} \\\\\dashrightarrow\sf Area\: of \:triangle =\sqrt{9 \times 4\times 4 \times 1} \\\\\dashrightarrow\sf Area \: of \: triangle = \sqrt{36 \times 4} \\\\\dashrightarrow\sf Area \: of \: triangle = \sqrt{6^2 \times 2^2} \\\\\dashrightarrow\sf Area \: of \: triangle = 6 \times 2 \\\\\dashrightarrow\large{\underline{\boxed{\rm{\red{Area\: of \: triangle = 12 \: cm^2 }}}}}$

$\therefore\underline{\textsf{Area \: of \: isosceles \: triangle = {\textbf{ 12 \: {cm}^{2} }}}}$