Question

What is the area of the given ΔABC?

Answer 1

Answer:

s=5+5+4/2

=14/2=7

area of triangle (herons formula)√s(s-a)(s-b)(s-c)

=√7(7-5)(7-5)(7-4)

=√7x2x2x3

=2√21cm²

Answer 2

Your Answer:

The following Question can be done by the concepts of Heron's formula

To apply this formula we have to find the semi perimeter first

Semi perimeter = a + b + c/2

So, Semi perimeter = 5+5+4/2

=> semi perimeter = 14/2 = 7

So, Heron's formula is

$\tt Area \ \ of \ \ triangle = \sqrt{s(s-a)(s-b)(s-c)} \\\\ \tt \Rightarrow Area = \sqrt{7(7-5)(7-5)(7-4)} \\\\ \tt \Rightarrow Area = \sqrt{7 \times 2 \times 2 \times 3} \\\\ \tt \Rightarrow Area =2\sqrt{21}cm^2$

So, Area of triangle is $\tt 2\sqrt{21} cm^2$

More to know:

• If any side is bigger than the semi perimeter. Then triangle is not possible.
• The above Question can also be solved by constructing a perpendicular bisector. As it is an isoceles triangle