Question

find the area of the following polygon

Answer 1

My friend ! I have already answered you. But still. 

First we will go step by step:

Find the length of  AL, LM, MN, NO, OD, ND so that it may be easy.

In Δ ALB, area = 1/2 bh = 1/2 * 10 cm * 30 cm = 150 cm² 

In Δ AMF, area = 1/2 bh = 1/2 * 20 * 20 = 200 cm²

In Δ EOD, area = 1/2 bh = 1/2 * OD * EO = 1/2 * 30 * 60 = 900 cm²

In Δ CND, area = 1/2 bh = 1/2 * CN * ND = 1/2 * 40 * 40 = 800 cm²

Now, in trapezium CBLN, 
height = 40 cm, both sides are 30 and 40 cm 
area =  1/2 h (sum of both sides)
1/2 * 40 * (30 + 40)
1/2 * 40 * 70 = 1400 cm²

Similarly to find area of trape. EFMN ,
1/2 * 30 * 80 = 1200cm²

Now, adding all these areas, we get :

(150 + 200 + 800 + 900 + 1400 + 1200)cm² = 4650 cm²

Hence area of the polygon is 4650 cm².