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## High school geometry

### Course: High school geometry>Unit 9

Lesson 2: Cavalieri's principle and dissection methods

# Cavalieri's principle in 2D

If two figures have the same height and the same width at every point along that height, they have the same area.

## Cavalieri's principle in 2D

Key idea: If two figures have the same $\text{height}$ and the same $\text{width}$ at every point along that height, they have the same $\text{area}$.
Wait a second, you already know this! Check it out.
What is the area of the rectangle?

What is the area of the parallelogram?

According to Cavalieri's principle, these figures have the same area because they have the same height $\left(6\right)$ and the same width $\left(4\right)$ as each other at every point along that height.

## Cavalieri's principle with varied widths

Sometimes a figure has different widths at different heights. Cavalieri's principle still works.
According to Cavalieri's principle, which of the following figures must have the same area?