Maths / Areas Of Parallelograms And Triangles / Figures on the Same Base and Between the Same Parallels

QUESTION

 In the given figure, if $\dpi{80} \large \dpi{110}l \left | \right |m,^{}$ then which of the following realtionship is true?
 OPTIONS A. ar($\dpi{80} \fn_phv \Delta$ABD)=ar($\dpi{80} \fn_phv \Delta$ACE) B. ar($\dpi{80} \fn_phv \Delta$ABE)=2ar($\dpi{80} \fn_phv \Delta ADE$) C. ar($\dpi{80} \fn_phv \Delta ABD)=2ar(\Delta AED)$ D. ar($\dpi{80} \fn_phv \Delta ABC)=ar(\Delta ABE)+ar(\Delta ACD-ar(\Delta ADE)$
Right Option : D

EXPLANATION
Explain TypeExplanation Content
Text

As $\dpi{80} \large \Delta ABE)\; and \;\Delta ACD \;have\; a \;common \;\Delta ADE$

so the area of triangle ADE is subtracted

$\dpi{80} \fn_phv ar(\Delta ABC)=ar(\Delta ABE)+ar(\Delta ACD-ar(\Delta ADE)$

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