Question

the adjoining figure ABCDEF is a hexagon. If AD=18 cm,AJ=15 cm, AI=12 cm, AH=8 cm, AG=5 cm, BG=3 cm, CI=5cm, JE=4 cm and HF=7 cm, then find its area.

Answer 1

Answer:

Area of ABCDEF is 123 sq.cm.

Step-by-step explanation:

Area of the hexagon = Area of ΔAGB + Area of ΔAHF + Area of trapezium BGIC + Area of trapezium HFEJ + Area of ΔCID + Area of ΔJED

Area of Triangle = (1/2) * Base * Height

Area of trapezium = (1/2)*(Base1+Base2) * Height

Area of ΔAGB = (1/2) * AG * BG = (1/2)*5*3=7.5 sq.cm.

Area of ΔAHF = (1/2)*AH*HF= (1/2)*8*7=28 sq.cm.

Area of BGIC = (1/2) * (BG+CI) *GI = (1/2)*(3+5)*(12-5)= 28 sq.cm.

Area of HFEJ = (1/2)*(HF+JE)*HJ=(1/2)*(7+4)*(15-8) = 38.5 sq.cm.

Area of ΔCID = (1/2)*ID*CI = (1/2)*(18-12)*5=15 sq.cm.

Area of ΔJED = (1/2)*JD*JE=(1/2)*(18-15)*4=6 sq.cm.

So, area of the hexagon = 7.5+28+28+38.5+15+6 = 123 sq.cm.

∴Area of ABCDEF is 123 sq.cm.

Answer 2

Answer:

the answer is 123 cm²

hope it helps