Areas of Plane Figures between Parallel Lines — O/L Mathematics

What must I remember about Areas of Plane Figures between Parallel Lines?

• Parallelograms on Same Base and Between Same Parallels: Parallelograms standing on the same base (or equal bases) and lying between the same pair of parallel lines are EQUAL IN AREA.
• Triangle and Parallelogram Relationship: The area of a triangle standing on the same base and between the same parallels as a parallelogram is exactly HALF the area of the parallelogram: Area(Δ) = (1/2) × Area(||gm).
• Triangles on Same Base and Between Same Parallels: Triangles standing on the same base (or equal bases) and lying between the same pair of parallel lines are EQUAL IN AREA.
• Converse Theorem: Triangles of equal area standing on the same base and on the same side of it lie between the same parallel lines.

Test yourself (1 minute)

1. Median of a Triangle divides Area in Half

   A median of a triangle connects a vertex to the midpoint of the opposite side, dividing the triangle into two sub-triangles of EQUAL AREA (same base length and same perpendicular height).

2. Trap of equal perimeter vs equal area

   Figures between parallel lines having equal areas DO NOT necessarily have equal perimeters.

3. Geometric construction proofs

   Adding a construction line parallel to a base is the standard technique to apply this theorem in riders.

Practise Areas of Plane Figures between Parallel Lines questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 8)

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Grade 11 · Term 1