Heron's formula allows us to calculate the area of a triangle when the height is unknown, using only the lengths of its sides. It involves calculating the semi-perimeter and subsequently applying the formula to find the area.
In this section, we explore Heron's formula, which calculates the area of a triangle given the lengths of its three sides, denoted as 'a', 'b', and 'c'. The formula is expressed as:
where s is the semi-perimeter given by
Heron's Formula: A method for calculating the area of a triangle given its side lengths.
Semi-Perimeter: The sum of the triangle's sides divided by two, needed for applying Heron's formula.
To find the area, follow this way, / Semi-perimeter first, then area to display.
Imagine a park in the shape of a triangle. You want to plant flowers but need to know how much space you have. Using Heron's formula helps you calculate the area quickly!
SAB: Semi-perimeter, Area, Base dimensions.
{'example': 'Find the area of a triangle with sides 40 m, 32 m, and 24 m.', 'solution': 'Given
{'example': 'Find the area of an equilateral triangle with side 10 cm.', 'solution': 'Here,
Term: Heron's Formula
Definition:
A mathematical formula that calculates the area of a triangle when the lengths of all three sides are known.
Term: SemiPerimeter
Definition:
Half the perimeter of a triangle, calculated as
Term: Area
Definition:
The measure of the space enclosed within a polygon.
Term: Scalene Triangle
Definition:
A triangle with all sides of different lengths.