Difference between revisions of "Parallelogram on same base and between same parallels have equal area"

Revision as of 15:16, 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.
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
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

@@ Line 17: / Line 17: @@
 # 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
-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
-ar (BCE) = ar (ADF) =  =
+#Proving that parallelograms on the same base and between the same parallels have equal area by using following calculations
-( 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)
-<nowiki>=             +           =</nowiki>
 Area of the parallelogram ABEF
 = Area of the Trapezium ABED  +  Area of the Triangle ADF
-ar (ABEF)  =  ar (ABED) + ar (ADF)
-<nowiki>=               +         =</nowiki>
-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.
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