Difference between revisions of "Parallelogram on same base and between same parallels have equal area"
From Karnataka Open Educational Resources
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=== Objectives === | === Objectives === | ||
+ | To verify that Parallelograms on the same base and between the same parallels are equal in area | ||
=== Estimated Time === | === Estimated Time === | ||
+ | 40 minutes | ||
=== Prerequisites/Instructions, prior preparations, if any === | === Prerequisites/Instructions, prior preparations, if any === | ||
+ | Knowledge about altitude, trapezium, congruent triangles, parallelogram and its area. | ||
=== Materials/ Resources needed === | === Materials/ Resources needed === | ||
− | Click here to [[:File:Areas of parallelograms on the same base bwtween the same parallels.ggb|open]] the file | + | Digital : Click here to [[:File:Areas of parallelograms on the same base bwtween the same parallels.ggb|open]] the file |
+ | |||
+ | Non-digital : Paper, pencil, ruler, compass, protractor | ||
=== Process (How to do the activity) === | === Process (How to do the activity) === | ||
− | {{Geogebra|kxre9cuf}} | + | {{Geogebra|kxre9cuf}}'''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 === | === 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 - [[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