# Activity 12F: Explaining Why the Area Formula for Triangles is Valid

PART A (RIGHT TRIANGLES) DIRECTIONS: In Part A, you will use the moving and additivity principles to explain in three ways why the following right triangle has area

## Way #1

Explain how the demonstration above shows that the area of a triangle is . Be sure to mention any principles of area helpful to your explanation.

## Way #2

Use the demonstration above to explain why the area of a triangle can also be thought of as . Be sure to mention any principles of area helpful to your explanation.

## Way #3

Use the demonstration above to explain why the area of a triangle can also be thought of as . Be sure to mention any principles of area helpful to your explanation.

PART B (ACUTE TRIANGLES) DIRECTIONS: ﻿In Part B, you will use the moving and additivity principles to explain in two ways why the acute triangle below has area

## Way #1

Use the demonstration above to explain why the area of a triangle can also be thought of as . Be sure to mention any principles of area helpful to your explanation.

## Way #2

Use the demonstration above to explain why the area of a triangle can also be thought of as . Be sure to mention any principles of area helpful to your explanation.

PART C (OBTUSE TRIANGLES) DIRECTIONS: Now, we will apply what we know about right triangles in order to prove the formula for the area of an obtuse triangle is also

Use the figure above AND what you know about right triangle areas to prove that the area of the purple obtuse triangle is also