ABCD is a trapezium show that area of trapezium ABCD is h/2 a + b
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Step-by-step explanation:
Prove that:
Area of a trapezium ABCD = {¹/₂ × (AB + DC) × h} square units.
Proof: Area of a trapezium ABCD
= area (∆DFA) + area (rectangle DFEC) + area (∆CEB)
= (¹/₂ × AF × DF) + (FE × DF) + (¹/₂ × EB × CE)
= (¹/₂ × AF × h) + (FE × h) + (¹/₂ × EB × h)
= ¹/₂ × h × (AF + 2FE + EB)
= ¹/₂ × h × (AF + FE + EB + FE)
= ¹/₂ × h × (AB + FE)
= ¹/₂ × h × (AB + DC) square units.
= ¹/₂ × (sum of parallel sides) × (distance between them)
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