Difference between revisions of "Parallelogram on same base and between same parallels have equal area"
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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, 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. | |
− | |||
− | AB ∥ FC and AB is the | ||
− | |||
− | Parallelograms ABCD and ABEF are | ||
− | |||
− | on the same base AB and between | ||
− | |||
− | same parallels AB and FC. | ||
− | |||
− | |||
Δ BCE ≅ Δ ADF (By SAS Congruence Criterion) | Δ BCE ≅ Δ ADF (By SAS Congruence Criterion) | ||
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=== Evaluation at the end of the activity === | === Evaluation at the end of the activity === | ||
− | + | # What is the relation between the area of a triangle and area of a parallelogram, if they lie on the same base and between the same parallel lines? | |
+ | # 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 ? | ||
+ | # In a parallelogram ABCD, AB = 7.2 cm and altitudes corresponding to sides AB and AD are respectively 10cm and 8cm. Find AD. | ||
Go back to the page - [[KVS Quadrilaterals|click here]] | Go back to the page - [[KVS Quadrilaterals|click here]] |
Revision as of 10:55, 5 September 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, 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.
Δ BCE ≅ Δ ADF (By SAS Congruence Criterion)
ar (BCE) = ar (ADF) = =
( Areas of Congruent figures are equal )
OBSERVATION / RESULT / OUTCOME :
Area of the parallelogram ABCD
= Area of the Trapezium ABED + Area of the Triangle BCE
ar (ABCD) = ar (BCE) + ar (ABED)
= + =
Area of the parallelogram ABEF
= Area of the Trapezium ABED + Area of the Triangle ADF
ar (ABEF) = ar (ABED) + ar (ADF)
= + =
Hence the theorem is verified.
Evaluation at the end of the activity
- What is the relation between the area of a triangle and area of a parallelogram, if they lie on the same base and between the same parallel lines?
- 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 ?
- In a parallelogram ABCD, AB = 7.2 cm and altitudes corresponding to sides AB and AD are respectively 10cm and 8cm. Find AD.
Go back to the page - click here