Difference between revisions of "Parallelogram on same base and between same parallels have equal area"
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=== Prerequisites/Instructions, prior preparations, if any === | === Prerequisites/Instructions, prior preparations, if any === | ||
− | Knowledge about altitude, congruent triangles, parallelogram and its area. | + | Knowledge about altitude, trapezium, congruent triangles, parallelogram and its area. |
=== Materials/ Resources needed === | === Materials/ Resources needed === | ||
Line 17: | Line 17: | ||
# Draw AB ∥ FC and AB is the base. | # 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. | # 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 | |
− | Δ BCE ≅ Δ ADF | + | #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 | |
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Area of the parallelogram ABCD | Area of the parallelogram ABCD | ||
− | = Area of the Trapezium ABED + Area of the Triangle BCE | + | = Area of the Trapezium ABED + Area of the Triangle BCE |
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Area of the parallelogram ABEF | Area of the parallelogram ABEF | ||
= Area of the Trapezium ABED + Area of the Triangle ADF | = Area of the Trapezium ABED + Area of the Triangle ADF | ||
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=== Evaluation at the end of the activity === | === Evaluation at the end of the activity === | ||
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# 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 ? | # 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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Go back to the page - [[KVS Quadrilaterals|click here]] | Go back to the page - [[KVS Quadrilaterals|click here]] | ||
+ | |||
+ | [[Category:Quadrilaterals]] |
Latest revision as of 13:43, 19 December 2020
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 ?
Go back to the page - click here