1. Click here to open the sketch
Circle
2. Drag (or animate) point "drag" along its segment. Observe how the polygon and the measures change.
3. Drag to give the polygon four or more sides.
Question 1. Each regular polygon with four or more sides is divided into triangles. look at the triangle with a thick outline. It has segments labeled a for apothem and s for side. The side is the base of this triangle and the length of the apothem is the height of the triangle. Write a formula for the area of the triangle using a and s.
When farmers Clarence and Mytle
died, they left their daughters their land with instructions to divide
it equally. One daughter, Ella, was considerably more conniving than her
sister, Jo. The land, unfortunately, was shaped as an irregular quadrilateral,
and it wasn't immediately obvious how to divide it equally. Ella first
tried to get Jo to agree to split it down the diagonal AC as shown, with
Ella getting region ACD and Jo getting region ABC. Jo could see that was
a bad deal.
Ella then offered to split the land
with both diagonals. Ella would take two regions, AED and BEC, leaving
Jo with regions ABE and CED. This sounded good to Jo, but when she checked
it out, she found that the sums of the regions were still not equal. "Ah,"
said Ella, "but the product of our regions are equal!"
This stumped Jo, and she agreed to the deal out of sheer awe for Ella's
discovery.