# Parallelogram on same base and between same parallels have equal area

From Karnataka Open Educational Resources

### Objectives

To verify that Parallelograms on the same base and between the same parallels are equal in area

### Estimated Time

40 minutes

### 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.

**Procedure :**

- 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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