A triangle problem from Cliff Pickover

Saw this problem on twitter this morning:

When I asked what the kids wanted to talk about today, my younger son said that he wanted to talk more about my the “things you should know” list that the math team from my older son’s school.

Well, that list had several ideas about areas of triangles, so I used the tweet as a starting point.

Here’s what each kid thought was the answer plus the calculation of the area of the first triangle:

In the last video my older son mentioned that we could also use Heron’s formula to calculate the area of the triangle. My younger son hasn’t seen that formula, yet, but I thought it would be fun to show him that formula:

Next we move to the other triangle and find the answer to the question in the Pickover tweet:

Finally, I thought it would be fun to look at Heron’s formula for a triangle whose area wasn’t so easy to calculate using other methods. I asked the boys to choose a random triangle and my younger son chose three sides that do not actually form a triangle (of course!).

That caused a fun little diversion at the beginning of this video, but once we worked through the area of that triangle we studied an actual triangle with Heron’s formula.

So, a quick little project using some triangle area formulas. Glad I saw the tweet from Cliff Pickover – it made motivating this project really easy.