Write a program to calculate the area of a triangle given...

Write a program to calculate the area of a triangle given the length of its three sides $-a, b,$ and $c-$ using these formulas:
\[
\begin{array}{c}
s=\frac{a+b+c}{2} \\
A=\sqrt{s(s-a)(s-b)(s-c)}
\end{array}
\]

Key Concepts

Heron's Formula

Heron’s Formula is a method for calculating the area of a triangle when the lengths of all three sides are known. It does not require knowing the height of the triangle. The formula uses the semiperimeter and gives the area as the square root of the product of the semiperimeter and the semiperimeter minus each side, making it a powerful tool in geometry for triangles where height is not readily available.

Semiperimeter

The semiperimeter of a triangle is defined as half the sum of the lengths of its three sides. It is a crucial intermediate value in Heron’s Formula, as it simplifies the computations required for determining the area of the triangle. This concept is widely used in geometry to make complex area calculations more manageable.

Transcript

00:01 Hello welcome to this lesson and this lesson will write a python program to calculate the area of a triangle giving the three sides a b and c all right so first of all let's have the side a so we convert it to floats and we say enter the length of side a right on the first side in the same way we have b we convert the equal to float then we say enter the length of side b alright then again we convert the side c also to a float so we say enter the length of side c let me fix something up here.

01:15 Then let's have x which is equal to the a plus b plus c divided by 2.

01:24 Okay.

01:25 Then now we can have the area which is equal to the whole of this to the the power 0 .5 which represent the square root of that okay then we can print the area of a triangle is this but before then i'll say the area of a triangle with sides then we'll have the a b and c so we'll have the area of the triangle go with sides a b and c okay is then we we have put the area okay so let's run to see the running game play my console suicide a less have five for it so i'd be less laughs around inside let's have eight all right this is a view of the time go aside five seven and eight is this right so let me bring a comma there so that it makes it redouble so between this i'm going to bring a comma all right all right so i have a b and c okay let's run again so have 15 15, 12, and 30.

04:25 It says the area with this is equal to c.

04:30 Okay.

04:31 So we can round the answer to any decimal place.

04:35 So for example, if we decide to round using round, rounding this to two decimal places...

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