Prove that the area of a trapezium is equal to half of the product of its height and sum of parallel sides.   - Zigya
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Prove that the area of a trapezium is equal to half of the product of its height and sum of parallel sides.  


Given: ABCD is a trapezium with AB || CD. AM is its height.


Given: ABCD is a trapezium with AB || CD. AM is its height.To Prove:

To Prove: ar(trapezium ABCD)

equals 1 half left parenthesis AB plus DC right parenthesis left parenthesis AM right parenthesis
Construction: Join AC Proof: ar(trapezium ABCD)
    
equals space ar space left parenthesis increment ADC right parenthesis plus ar left parenthesis increment ABC right parenthesis
equals space 1 half cross times DC cross times AM plus 1 half cross times AB cross times AM
equals space 1 half cross times left parenthesis DC plus AB right parenthesis cross times AM
equals space 1 half open parentheses AB plus DC close parentheses left parenthesis AM right parenthesis
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