Here's the whole idea in one breath: a triangle is half a rectangle. Find the rectangle it's hiding in, work out that rectangle's area the easy way, then cut it in half. Done.
Start with What You Already Own
You already know how to find the area of a rectangle — you count how many unit squares fit inside it, which is just length × width. An 8-by-6 rectangle holds 48 little squares. Easy, and it never lets you down.
A triangle feels harder because it has a slanted side, and you can't neatly tile a slope with squares. So instead of fighting the slope, we do something sneaky: we trap the triangle inside a rectangle and use what we already know.
The Two Words That Do All the Work
The base is the side you sit the triangle on. The height is not the slanted side — it's how far straight up the top point is from that base, at a perfect right angle. Most mistakes come from reading the slope as the height, so say it twice: height goes straight up, not along the slope.
The rectangle around the triangle is base wide and height tall, so its area is base × height, and the triangle is half of it:
Press “Fold it into a rectangle” in the toy and watch a second copy of the triangle rotate round and click into the empty space, completing the rectangle. Two triangles make one rectangle — so one triangle is half. That's the whole proof, and now you've seen it with your own eyes.