1
Area(△EBC) = Area(ABCD)
2
Area(ABCD) = Area(△ABC) + Area(△ACD)
FORMULA CHAPTER
Chapter 14 – Construction of an Equal-Area Triangle
WBBSEClass 09Mathematics2 formulas
Complete WBBSE Madhyamik Class 9 equal-area triangle construction guide with area decomposition, notation and step-by-step examples for exam preparation.
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Equal-Area Triangle Construction Condition
Area(△EBC) = Area(ABCD)
SymbolMeaningUnit
ABCDGiven quadrilateralNot applicable
△EBCConstructed equal-area triangleNot applicable
DE ∥ ACParallel-line construction conditionNot applicable
Worked example
Question: Quadrilateral ABCD has area 54 cm². Triangle EBC is constructed by the standard parallel-line method to be equal in area to ABCD. Find Area(△EBC).
Calculation:
Step 1: Area(ABCD) = 54 cm².
Step 2: The construction preserves the total area.
Step 3: Area(△EBC) = Area(ABCD) = 54 cm².
Answer: Area(△EBC) = 54 cm².
Quadrilateral Area by a Diagonal
Area(ABCD) = Area(△ABC) + Area(△ACD)
SymbolMeaningUnit
ABCDGiven quadrilateralNot applicable
ACDiagonal of the quadrilaterallength units
△ABC, △ACDTwo component trianglesNot applicable
Worked example
Question: Diagonal AC divides quadrilateral ABCD into triangles of areas 24 cm² and 18 cm². Find Area(ABCD).
Calculation:
Step 1: Area(△ABC) = 24 cm².
Step 2: Area(△ACD) = 18 cm².
Step 3: Area(ABCD) = 24 + 18 = 42 cm².
Answer: Area(ABCD) = 42 cm².