Question

an) Find the area of polygon MNOPQR (Fig 11.19) if
MP=9 cm, MD=7 cm, MC = 6 cm, MB = 4 cm,
MA= 2 cm
NA, OC, QD and RB are perpendiculars to
diagonal MP.
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Answer 1

Step-by-step explanation:

Firstly, we will calculate the area of all the Triangles and trapezium present in the polygon MNOPQR and then we will add them.

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Answer 2

Area of Polygon MNOPQR=31.75 square cm

Step-by-step explanation:

In Polygon MNOPQR

MP=9 cm

MD=7 cm

DP=MP-MD=9-7=2 cm

MC=6 cm

CD=MD-MC=7-6=1 cm

CP=CD+DP=1+2=3 cm

MB=4 cm

BC=MC-MB=6-4=2 cm

MA=2 cm

AB=MB-MA=4-2=2 cm

NA=2.5 cm

OC=3 cm

QD=2 cm

RB=2.5 cm

AC=AB+BC=2+2=4 cm

BD=BC+CD=2+1=3 cm

Area of triangle=$\frac{1}{2}\times Base\times height$

Area of trapezium=$\frac{1}{2}(sum\;of\;parallel\;sides)\times height$

Area of Polygon MNOPQR=ar(MAN)+ar of trapezium(ACON)+ar(OCP)+ar(MBR)+ar of trapezium(BRQD)+ar(QDP)

Area of Polygon MNOPQR=$\frac{1}{2}(2)(2.5)+\frac{1}{2}(2.5+3)(4)+\frac{1}{2}(3)(3)+\frac{1}{2}(4)(2.5)+\frac{1}{2}(2.5+2)(3)+\frac{1}{2}(2)(2)$

Area of Polygon MNOPQR=2.5+11+4.5+5+6.75+2=31.75 square cm

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