Area of a Triangle — Half the Rectangle

Two right triangles stacked form a rectangle. Any triangle, rotated and matched with a copy, does the same. The child sees this geometrically: the triangle is half the rectangle. The insight generates the formula.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Geometry
• Level: Ages 7-8

Objectives

• Discover that a triangle is half of a rectangle sharing its base and height
• Derive the formula A = ½ × b × h
• Compute triangle areas
• Extend to all triangle types

Materials

• Right triangles cut from paper
• Matching rectangles (same base, same height)
• Rulers
• Calculator

Instructions

1. Cut a right triangle from paper, base 4, height 3. 2. Cut a matching rectangle 4 × 3. 3. Place two right triangles together — they form the rectangle. 4. Rectangle area = 12. 5. Triangle area = 6 = ½ × 12. 6. Derive: Atriangle = ½ × b × h. 7. Apply to a scalene triangle: compute using the formula. 8. Verify by drawing on grid paper. 9. Compute the area of a triangle cut from cloth or cardboard.

Educator tip

The two-triangle-equals-rectangle demonstration is the whole lesson. Once seen, the formula is unforgettable.

Assessment

Note derivation understanding and formula application.

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