Day 2 Activities

Paper tearing activity: Students will create a rectangle of their choice. After discussing the area of a rectangle, students will tear their rectangle in half, This will be done by tearing along a diagonal of the rectangle. Students will notice that the area of each triangle is the same, thus discovering a formula for the area of a triangle.

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Pick's Formula: Area of a triangle equals the number of points which lies on the border plus the number of points which lie within the border minus 1 (this is when the triangle is placed on a grid like a geoboard).

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Exercises:

Solve for the area of the following polygons:

 

For each of the following triangles, Use Pick's Formula for finding its area.

10.11.12.

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CHALLENGE #1:

Find some other method used to find the area of a triangle, besides a=1/2(base)(height) or Pick's Formula. Below are some possibilities:

Heron's Formula

Area of Circumscribed rectangle

Use of Vectors

CHALLENGE #2:

Develop on your own, a new method for finding the area of a triangle.

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ASSIGNMENT:

Write a short essay on how the area of a triangle and a rectangle relate.

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