## 6.1: Mental Calculations

Find a strategy to make each calculation mentally:

- $599 + 87$
- $254 - 88$
- $99 \boldcdot 75$

Let’s estimate the areas of weird shapes.

Find a strategy to make each calculation mentally:

- $599 + 87$
- $254 - 88$
- $99 \boldcdot 75$

Here is a floor plan of a house. Approximate lengths of the walls are given.

What is the approximate area of the home, including the balcony? Explain or show your reasoning.

Estimate the area of Nevada in square miles. Explain or show your reasoning.

We can find the area of some complex polygons by surrounding them with a simple polygon like a rectangle. For example, this octagon is contained in a rectangle.

We can estimate the area of irregular shapes by approximating them with a polygon and finding the area of the polygon. For example, here is a satellite picture of Lake Tahoe with some one-dimensional measurements around the lake.

The area of the rectangle is 160 square miles, and the area of the triangle is 17.5 square miles for a total of 177.5 square miles. We recognize that this is an approximation, and not likely the exact area of the lake.

Aerial photo of Lake Tahoe Copyright Owner: US Geological Survey License: Public Domain Via: US Geological Survey