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Line 17: − + − + − + − ar (BCE) = ar (ADF) = =+ − + − ( Areas of Congruent figures are equal ) − − OBSERVATION / RESULT / OUTCOME : − − + − − ar (ABCD) = ar (BCE) + ar (ABED) − − <nowiki>= + =</nowiki> − − ar (ABEF) = ar (ABED) + ar (ADF) − − <nowiki>= + =</nowiki> − − Hence the theorem is verified. − # 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? − # In a parallelogram ABCD, AB = 7.2 cm and altitudes corresponding to sides AB and AD are respectively 10cm and 8cm. Find AD. + +
Parallelogram on same base and between same parallels have equal area (view source)
Revision as of 13:43, 19 December 2020
, 13:43, 19 December 2020added Category:Quadrilaterals using HotCat
=== 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 ===
# 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 (By SAS Congruence Criterion)
#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 parallelogram ABCD
= Area of the Trapezium ABED + Area of the Triangle BCE
= Area of the Trapezium ABED + Area of the Triangle BCE
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
=== 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 ?
# 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]]
Go back to the page - [[KVS Quadrilaterals|click here]]
[[Category:Quadrilaterals]]