# Finding Area in Different Ways: Math Task

1. Here are three polygons: a)  Using any method you want, calculate the area of each polygon.

b)  Describe at least 3 methods for calculating the area of polygon b.

c)  Will these methods work to calculate the areas of polygons a and c? Explain why or why not.

2. Two vertices of a triangle are located at (0, 4) and (0,10). The area of the triangle is 12 units2. a)  What are all possible positions for the third vertex?

b)  Explain how you know these vertices create triangles with an area of 12
units2. Write a convincing mathematical explanation.

c)  How do you know there aren't any more?

d)  How many right triangles are there? List the coordinates of the third vertex
for each of the right triangles.

e)  How many isosceles triangles are there? List the coordinates of the third
vertex for each of the isosceles triangles.

f)  After answering parts d and e, do you want to make any changes to your answer
to part a? If so, what changes do you want to make?

© 2008 by Education Development Center, Inc. from The Fostering Geometric Thinking Toolkit. Portsmouth, NH: Heinemann. Reproduced with permission.