Question

- State Heron's Area Formula and the requirements needed to use the formula. - Research the Greek Mathematician Heron of Alexandria and one interesting fact that you discovered about him.

Answer 1

Heron's Area Formula, A=√[s(s-a)(s-b)(s-c)], calculates the triangle's area using side lengths a, b, and c, with s being the semi-perimeter. Heron of Alexandria, a Greek mathematician, not only provided this formula but also engineered automatic machines.

Step-by-step explanation:

Heron's Area Formula

Heron's Area Formula is used to calculate the area of a triangle when the lengths of its three sides are known. The formula is given by A = √[s(s-a)(s-b)(s-c)], where A is the area of the triangle, a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter of the triangle, calculated as s = (a + b + c) / 2. The requirements to use this formula are simply the measurements of all three sides of the triangle, and that the side lengths must satisfy the triangle inequality theorem so that a valid triangle is formed.

Heron of Alexandria

Heron of Alexandria was a Greek mathematician and engineer who lived around the 1st century AD. One interesting fact about Heron is that aside from his famous formula for calculating the area of a triangle, he also built a variety of machines, including mechanisms that could automatically open temple doors or dispense water, showcasing his engineering prowess alongside his mathematical contributions.

Answer 2

Heron's formula

Heron's formula is used to find the area of a triangle that has three different sides. Heron's formula is written as:

`A\text{ = }√(s(s-a)(s-b)(s-c))`

where a, b and c are the sides of the triangle, and s is the semi perimeter of the triangle.

Requirement to use Heron's formula:

The three side length of the triangle must be known

Interesting Fact Heron of Alexandria

Heron’s most important geometric work, Metrica, was lost until 1896. It is a compendium, in three books, of geometric rules and formulas that Heron gathered from a variety of sources, some of them going back to ancient Babylon, on areas and volumes of plane and solid figures. The book enumerates means of finding the area of various plane figures and the surface areas of common solids. Included is a derivation of Heron’s formula (actually, Archimedes’ formula) for the area A of a triangle.