Mensuration

Question

Find the area of polygon MNOPQR if MP = 9 cm, MD = 7 cm, MC = 6 cm, MB = 4 cm, MA = 2cm. NA, QC, QD and RB are perpendiculars to diagonal MP.

Solution

Area of polygon MNOPQR
= $WiredFaculty$
∵ Area of $increment space MAN$ = $WiredFaculty$
= $1 half cross times 2 cross times AN space cm squared space equals space AN space cm squared$
Area of trapezium ACON = $1 half left parenthesis AN plus OC right parenthesis cross times AC$
$equals space 1 half left parenthesis AN plus OC right parenthesis space cross times space left parenthesis MC minus MA right parenthesis$
$equals space 1 half left parenthesis AN plus OC right parenthesis space cross times space left parenthesis 6 minus 2 right parenthesis$
$equals space 1 half left parenthesis AN plus OC right parenthesis cross times 4 space equals space 2 left parenthesis AN plus OC right parenthesis cm squared$
WiredFaculty