Question

20) Find the area of polygon MNOPQR if O 3CM N 2.5 cm 2.5 cm - B D M P С IL 2 cm 2.5 cm Q R. = = MP = 9 cm, MD = 7cm , MC =6 cm , MB = 4 cm, MA = 2cm, NA, OC , QD and RB are perpendiculars to diagonals MP.​

Answer 1

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Find the area of polygon MNOPQR 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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Solution

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AB=MB−MA=4−2=2cm

AC=MC−MA=6−2=4cm

BD=MD−MB=7−4=3cm

CP=MP−MC=9−6=3cm

DP=MP−MD=9−7=2cm

Area of trapezium=

2

1

h(a+b), where a and b are parallel sides and h is the height of the trapezium.

Area of triangle=

2

1

bh where b is the base of the triangle and h is the height of the triangle.

Area(MNOPQR)=Area(MNA)+Area(ANOC)+Area(COP)+Area(DQP)+Area(BRQD)+Area(MBR)

⇒Area(MNOPQR)=

2

1

(2×2.5+4×(3+2.5)+3×3+2×2+3×(2+2.5)+4×2.5)

⇒Area(MNOPQR)=

2

1

(5+22+9+4+13.5+10)=

2

63.5

cm

2

=31.75cm

2