Math 101 Assignment 1

Junqian Hu (22689160) —- Sylvia

Manni Zhang (45580164) —- Manni

Yilun Yang (24307167) —- Alan

Part 1: Short Story

Jennie and John are the newlyweds and they plan to construct their house by themselves. Jennie chooses a special type of window with an arched side on top. When they choose the real style, one question comes up: what is the area of their window?

Smart Jennie noticed the small gratings on the window. She says: “Why don’t we divide the windows into small parts and add them up?” She divides the window into two parts: a regular rectangle below and an irregular shape above with an arched top side. Then she divides the above shape into 4 gratings and seems the irregular shapes as regular small rectangles. Approximately, the whole area of the window comes out.

Part 2: Further Explanation

We wanna know the area of this irregular shape, we will cut this area into small pieces of “rectangles” and then find a point from the curve side assume the length from the opposite side of rectangle be the height so that we can calculate the area of each rectangle. Add them up, we can get an approximate value of the area that the irregular shape owned. However, the we don’t think the value is precise enough, we decide to get more small pieces. As more and more pieces we get the more and more accurate the value we get.

As you can see from the graph, the total area of the rectangles nearly equals to the area of the shape.