Question

10. Give a brief biography of Heron of Alexandria stating where he lived, when he lived, what he did to earn the name attached to this formula and what an Aeolipile (or Hero's Engine) is. 11. State 3 real-life situations it would be useful to use Heron's Formula instead of the A = bh/2 area formula?

Answer 1

The answer is:

1° a lake that you want to measure the size of. You can create triangles that encompass the lake, but you can’t effectively measure the distance across the lake to the opposing shore at the point where the perpendicular meets the opposing side.

2° imagine a case where you are surveying a piece of land, but there is a building in the center where you cannot measure the perpendicular through it, but you can measure the sizes of triangles that encompass it. So you can measure the edges, but not the perpendicular.

3° Imagine a field whose area has to be calculated accurately.