Question

Fig. 14.26
14. Find the area of the hexagon TAGORE, if TO = 9 cm, TS = 7 cm,
TH = 6 cm, TF = 4 cm, TB = 2 cm, AB = 3 cm, GH = 5 cm,
SR = 2 cm and EF = 4 cm.​

Answer 1

Given : hexagon TAGORE,  

TO = 9 cm, TS = 7 cm, TH = 6 cm, TF = 4 cm, TB = 2 cm, AB = 3 cm, GH = 5 cm, SR = 2 cm and EF = 4 cm.​

To Find :  Area of the Hexagon TAGORE

45.5 cm²

46.5 cm²

47.5 cm²

Solution:

 Area of the Hexagon TAGORE = Ar Δ TBA + Ar Trapezium ABHG +  Ar Δ GHO +  Ar Δ TFE + Ar Trapezium FERS +  Ar Δ OSR

Ar Δ TBA  = (1/2) * TB * AB = (1/2) * 2 * 3  = 3  cm²

Ar Trapezium ABHG  = (1/2) (AB + GH) BH  = (1/2) (3 + 5) (6 - 2)  = 16 cm²

Ar Δ GHO  = (1/2) GH * OH = (1/2) * 5 * (9 - 6)  = 7.5   cm²

Ar Δ TFE =  (1/2) * TF * EF  =  (1/2) * 4 * 4  = 8   cm²

Ar Trapezium FERS = (1/2) (EF + RS) * FS = (1/2)(4 + 2)(7 - 4)  = 9 cm²

 Ar Δ OSR = (1/2) SO * SR = (1/2) (9 - 7) * 2  = 2  cm²

 Area of the Hexagon TAGORE = 3 +16 + 7.5 + 8 + 9 + 2

= 45.5  cm²

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Answer 2

Answer:

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