Inthebelowfigure,ABCDisaquadrilateralandBE||ACandalsoBEmeetsDCproducedatE.
ShowthatareaofADEisequaltotheareaofquadrilateralABCD.
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007shiva:
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given: BEIIAC
=> ABCD IS A IIGM [OPP. SIDES OF A IIGM ARE EQUAL]
=> arΔ ABC = ar ΔACE (AREA B/W SAME BASE AND SAME II LINE AC AND BE)
=> BY ADDING ar ADC TOBOTH SIDES WE GET,
=> ar ΔABC +ar ΔADC =arΔ ACE+ ar ΔADC
=> ar quad abcd =arΔ ADE
HP
=> ABCD IS A IIGM [OPP. SIDES OF A IIGM ARE EQUAL]
=> arΔ ABC = ar ΔACE (AREA B/W SAME BASE AND SAME II LINE AC AND BE)
=> BY ADDING ar ADC TOBOTH SIDES WE GET,
=> ar ΔABC +ar ΔADC =arΔ ACE+ ar ΔADC
=> ar quad abcd =arΔ ADE
HP
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