Given a triangle with the following measurements,
Basis=$$11$$ cm, side 1 $$= 11$$ cm, side 2 $$=7,5$$ cm, height (h) $$=7$$ cm
calculate the area using the Heron's formula.
See development and solution
Development:
First we proceed to calculate the semiperimeter.
The information of the statement interpreted by our formula is:
$$a=11, b=11, c=7,5$$
Then we have: $$p=\dfrac{a+b+c}{2}=\dfrac{11+11+7,5}{2}=14,75$$
Applying it to Heron's formula:
$$A=\sqrt{p(p-a)(p-b)(p-c)}=$$ $$=\sqrt{14,75 \cdot (14,75-11) \cdot (14,75-11) \cdot (14,75-7,5)}=38,5\ \mbox{cm}^2$$
Solution:
$$38,5 \ \mbox{cm}^2$$