Top surface of a raised platform is in the shape of a regular octagon

1.	Top surface of a raised platform is in the shape of a regular octagon as shown in Fig. 11.29(a). Find the area of the octagonal surface.
Answer» $\huge \bf\underline\red{Question}$ Top SURFACE of a raised platform is in the SHAPE of a regular octagon as SHOWN in Fig. 11.29(a). Find the area of the octagonal surface. $\huge \bf\underline\red{Solution}$ $\sf \red {In \: Fig (b), Area \: of \: one \: trapezium \: ABGH}$ $= \: 12 (AH+BG) \times AM$ $= \frac{1}{2} (5 + 11) \times 4 = \frac{1}{2} \times 16 \times 4$ $= 32m {}^{2}$ $\sf \red {Area \: of \: rectangle \: BCFG = \: l \times b}$ $= 11 \times 5 = 55m {}^{2}$ $\sf \red {Area \: of \: Another \: trapezium \: CDEF}$ $= \frac{1}{2} (DE +CF) \times DN$ $= \frac{1}{2} (5 + 11) \times 4 = \frac{1}{2} \times 16 \times 4$ $= 32 m {}^{2}$ $\sf \red{→Area \: of \: Octagonal \: surface \: =}$ $\sf \red { Ar. \: of \: ABGH + Ar. \: of \: BCFG + Ar. \: of \: CDEF}$ $= (32 + 55 + 32)m {}^{2} = 119m {}^{2}$ $\sf \blue {Hence \: Answer is \: 119m {}^{2} }$ $\bf\underline\red{Hope \: It \: Helps \: You!}$