Parallelogram on same base and between same parallels have equal area
To verify that Parallelograms on the same base and between the same parallels are equal in area
Prerequisites/Instructions, prior preparations, if any
Knowledge about altitude, trapezium, congruent triangles, parallelogram and its area.
Materials/ Resources needed
Digital : Click here to open the file
Non-digital : Paper, pencil, ruler, compass, protractor
Process (How to do the activity)
Download this geogebra file from this link.
- Draw AB ∥ FC and AB is the base.
- Draw Parallelograms ABCD and ABEF are on the same base AB and between same parallels AB and FC.
- Identifying plane figures on the same base and between the same parallels
- Identify Congruent triangles i.e. Δ BCE ≅ Δ ADF and find the area of triangles
- Find the area of Trapezium ABED by using finding an area tool
- What can you say about their areas?
- Proving that parallelograms on the same base and between the same parallels have equal area by using following calculations
Area of the parallelogram ABCD
= Area of the Trapezium ABED + Area of the Triangle BCE
Area of the parallelogram ABEF
= Area of the Trapezium ABED + Area of the Triangle ADF
Evaluation at the end of the activity
- If one rectangle and one parallelogram lying on the same base and between the same parallel lines then what will be area of the rectangle ?
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