# Discover the Area Formula for a Triangle

Topic:
Area

## Instructions

The area of a triangle is determined by finding out how many unit squares it takes to fill in the triangle, just like all other polygons. Triangles do not have easy to count units though, because of the angles. We know that the area of a triangle can be related to the area of a rectangle. So going off of that, maybe the formula for the area of a triangle is somehow related to the formula for the area of a rectangle.

What is the formula for the area of a rectangle?

## Generating Data on Triangles and Their Area

You will be generating different sized triangles using GeoGebra. Each of the triangles must have different heights and bases. Use your mouse to move the blue and red points of the triangle.

## Data Table

Include 6 Triangles (Label them Triangle 1, Triangle 2, etc) ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿Triangle: ﻿ ﻿ ﻿Base in Units: ﻿ ﻿ ﻿ ﻿Height in Units: ﻿ ﻿ ﻿ ﻿Area in Unit Squares:

## Search for a Pattern

If you know the triangle's height and base, how could you compute the area without counting the square units?

Describe your method and write a formula:

## Test It Out

Check to see if your formula works with the following base and heights. Double check by using the GeoGebra Application. Triangle A: Base=4 Height=1 Triangle B: Base=10 Height=7 Triangle C: Base=6 Height=9 Did your formula work? If not, what do you think went wrong?