Question

Find the area of polygon PQRSTUV where, PR=10cm, QV=5cm, TU=4cm, TS=6cm

Answer 1

Step-by-step explanation:

AD = 10 cm, AG = 8 cm, AH = 6 cm, AF = 5 cm

BF = 5 cm, CG = 7 cm, EH = 3 cm

Therefore, FG = AG – AF = 8 – 5 = 3 cm

And, GD = AD – AG = 10 – 8 = 2 cm

From given figure:

Area of Pentagon = (Area of triangle AFB) + (Area of trapezium FBCG) + (Area of triangle CGD) + (Area of triangle ADE)= (12x AF x BF) + [12 x (BF + CG) x (FG)] + (12 x GD x CG) + (12 x AD x EH).

= (12 x 5 x 5) + [12 x (5 + 7) x (3)] + (12 x 2 x 7) + (12 x 10 x 3)

= (252) + (362) + (142) + (302)

= 12.5 + 18 + 7 + 15 = 52.5 cm2