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Guiding Question: In what ways can shapes be related by using conservation of area?
triangles
triangles
The "Half" Rule: Any triangle is exactly half of a parallelogram that has the same base and height.
The Formula: Area = (base x height) รท 2 (A = bh รท 2)
Same Area, Different Look: If two triangles have the same base and height, they have the same area, even if one looks "tilted" and the other is a right triangle.
parallelograms
parallelograms
A 4-sided shape (quadrilateral) where opposite sides are parallel and equal in length.
Base & Height: You can pick any side to be the base. The height is the perpendicular distance (a straight 90ยฐ line) from that base to the opposite side.
Common Mistake: The height is not the slanted side!
The Formula: Area = base x height (A = bh)
The Secret: If you cut a triangle off one side (as shown above) and slide it to the other side, it forms a perfect rectangle. This is why the formula is the same!
Composite Shapes
Composite Shapes
A "composite" shape is just a big shape made of smaller ones (like a house made of a square and a triangle).
Decomposing: You can find the total area by "breaking" the shape into smaller triangles and parallelograms, finding their areas separately, and adding them together.
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