What is the answer of ncert maths book class 8, ch. MENSURATION pg 176, TRY THESe Q. 3 For future i would like to know where can i get the answers of try these of ncert book

Given : NA, OC, QD and RB are perpendiculars to diagonal MP 

and MP = 9 cm, MD = 7 cm, MC = 6 cm, MB = 4 cm, MA = 2 cm

⇒ AC = MC - MA = 6 cm - 2 cm = 4 cm

BD = MD - MB = 7 cm - 4 cm = 3 cm

CP = MP - MC = 9 cm - 6 cm = 3 cm

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

Also, NA II OC II QD II RB

Now, ar (ΔMAN) = 1/2 × NA × MA = 1/2 × 2.5 cm × 2 cm = 2.5 cm2

ar (ΔMBR) = 1/2 × RB × MB = 1/2 × 2.5 cm × 4 cm = 5 cm2

ar (ΔPQD) = 1/2 × QD × DP = 1/2 × 2 cm × 2 cm = 2 cm2

ar (ΔPOC) = 1/2 × OC × CP = 1/2 × 3 cm × 3 cm = 4.5 cm2

ar (trapezium ACON) = 1/2 × (NA + OC) × AC = 1/2 × (2.5 cm + 3 cm) × 4 cm = 11 cm2

ar (trapezium BDQR) = 1/2 × (RB + QD) × BD = 1/2 × (2.5 cm + 2 cm) × 3 cm = 6.75 cm2

Hence, ar (polygon MNOPQR) = ar (ΔMAN) + ar (ΔMBR) + ar (ΔPQD) + ar (ΔPOC) + ar (trapezium ACON) + ar (trapezium BDQR) 

= 2.5 cm2 + 5 cm2 + 2 cm2 + 4.5 cm2 + 11 cm2 + 6.75 cm2 = 31.75 cm2

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