Area of a Triangle

Relationship between Rectangle and Triangle

If you draw a diagonal across a rectangle, you divide it into two identical triangles.

• The two triangles overlap exactly.
• Therefore, their areas are equal.
• Area of each triangle = $\frac{1}{2} \times$ Area of the Rectangle.

Generalizing for Any Triangle

Even if the triangle is not a right-angled triangle (formed by the diagonal of a rectangle), we can often split it or box it into rectangles to find its area.

Key Concept: The area of a triangle is half the product of its base and the perpendicular height.

(Note: In this specific chapter, the text focuses heavily on the grid method and the “half-rectangle” concept rather than just memorizing the $1/2 \times b \times h$ formula immediately, encouraging visual understanding.)