Question

find the area of the Pentagon ABCD,if AD=8cm,AH=6cm,AG=4cm,AF=3cm,BF=2cm,CH=3cm and EG=2.5cm.​

Answer 1

Answer:

23.5 cm^2

Step-by-step explanation:

area of Triangle AED = 1/2 base × height

= 1/2 × Ad × EG

= 1/2 × 8 × 2.5

= 2.5×4

= 10 cm^2

Fh = Ah - Af = 6-3 = 3cm

Area of Trapezium BFCH = 1/2(sum of parallel sides) ×h

= 1/2 × (BF + CH) × FH

= 1/2 × (2 + 3) × 3

= 15/2 = 7.5 cm^2

Area of triangle ABF = 1/2 × BF × AF

= 1/2 × 2 × 3 = 3cm^2

DH = AD - AH = 8 - 6 = 2cm

Area of triangle CHD = 1/2 CH × DH

1/2 × 3 × 2 = 3cm^2

Area of Pentagon ABCD = ar(AED) + ar(ABF) + ar(CHD) + ar(BFCH) = 10+ 7.5+ 3+3 = 23.5 cm^2