📏 Area of Triangles & Parallelograms

What is Area?
Area is the amount of space inside a 2-dimensional shape. It is measured in square units (cm², m², in², etc.).
Why is Triangle Area Formula ½ × base × height?
A triangle is exactly half of a parallelogram (or rectangle) with the same base and height!
Rectangle area = base × height
Triangle area = ½ × base × heightImportant Notes:
• Base can be any side of the triangle
• Height must be perpendicular (straight up/down) to the base
• Height is NOT the slanted side!

What is a Parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides.
Why is Parallelogram A = b × h?
A parallelogram can be transformed into a rectangle with the same base and height!
Cut here → ┌────────────┐
│ │
│ │ Move triangle
│ │ to other side
└────────────┘

┌────────────┐
│░░░░░░░░░░░░│ → ┌────────────┐
│░░░░░░░░░░░░│ │░░░░░░░░░░░░│
└────────────┘ └────────────┘
┌────────────┐
│ │
│ │
└────────────┘

Result: Rectangle with same base and height!Important Notes:
• Height must be perpendicular to the base
• Height is NOT the slanted side length
• Base can be any side of the parallelogram

What is an Irregular Polygon?
An irregular polygon is a shape that is not a standard shape like a triangle, square, or rectangle. The sides are not all equal, and angles may vary.
Two Methods to Find Area:
MethodDescriptionWhen to UseDecomposingBreak shape into smaller shapes (triangles, rectangles)Shape has "indents" or can be split easilyComposingAdd extra shapes to form a larger shape, then subtractShape has "missing pieces"Strategy:
• Look for ways to split the shape into rectangles, triangles, and parallelograms
• Find area of each part
• Add all areas together