★ Must-know
📌 Figures that can be placed exactly on top of one another have the same area.
A figure's area can be found by decomposing it into pieces, rearranging the pieces into known shapes, finding their areas, and adding them.
A figure's area can be found by calculating the area of a containing shape and subtracting the area of the missing piece.
Further detail
1. What does it mean to tile a two-dimensional region?
2. A student wants to begin investigating which of two patterns covers more of a plane. What is a useful first approach?
3. Two figures can be placed exactly on top of one another. What conclusion follows about their areas?
What does tiling a two-dimensional region involve?
Covering it with copies of the same shape or shapes without gaps or overlaps.
What do figures that fit exactly on top of one another have in common?
They have the same area.
How can a figure’s area be found by rearranging its pieces?
Find the areas of the rearranged known shapes and add them.
How can a figure’s area be found using a containing shape?
Subtract the missing piece’s area from the containing shape’s area.
What defines a parallelogram’s opposite sides?
They are parallel and equal in length.
What relationship do a parallelogram’s opposite angles have?
They have equal measures.
It covers the core concepts of Area and Volume Geometry, organized by topic with the key definitions, explanations and takeaways, so it's easier to learn and remember.
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