Lesson 2: Area - Estimation

   Constructing Knowledge

Area can be calculated with formulas, but sometimes an estimated area is all that is needed. Before purchasing materials such as hardwood flooring or sod for a back yard, an estimation of how much is needed can be made.

One method for estimating area involves using grid paper and then using an average of the overestimation and underestimation of the area of the shape. Estimating is commonly used when the desired area cannot easily be calculated using the formulas used throughout this lesson. This is particularily relevant for oddly-shaped yards or rooms in a home.

   Multimedia

A video describing FILL IN is provided.



An underestimation of a shape's area is when you count only the full squares on the grid inside of the shape's outline. The underestimation of the black rectangle's area is 28 squares (a 7 × 4 rectangle).



An overestimation of a shape's area is when you count any square that part of the shape is touching. The overestimation of the black rectangle's area is 54 squares (a 9 × 6 rectangle)



The estimated area of the rectangle is the average of the underestimation and overestimation.

To calculate average:
Add all the values together, and then divide by the number of values used.

\(\begin{align} \text{A}_{\text{estimate}}&=\frac{\left(\text{underestimate}+\text{overestimate}\right)}{2} \\ \\ \text{A}_{\text{estimate}}&=\frac{\left(\text{28 squares}+\text{54 squares}\right)}{2} \\ \\ \\ &=41\,\text{squares} \end{align}\)

The estimated area of this rectangle is 41 squares.


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