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.​

Answer 1

$\huge \bf\underline\red{Question}$

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.

$\huge \bf\underline\red{Solution}$

$\sf \red {In \: Fig (b), Area \: of \: one \: trapezium \: ABGH}$

$= \: 12 (AH+BG) \times AM$

$= \frac{1}{2} (5 + 11) \times 4 = \frac{1}{2} \times 16 \times 4$

$= 32m {}^{2}$

$\sf \red {Area \: of \: rectangle \: BCFG = \: l \times b}$

$= 11 \times 5 = 55m {}^{2}$

$\sf \red {Area \: of \: Another \: trapezium \: CDEF}$

$= \frac{1}{2} (DE +CF) \times DN$

$= \frac{1}{2} (5 + 11) \times 4 = \frac{1}{2} \times 16 \times 4$

$= 32 m {}^{2}$

$\sf \red{</strong><strong>→</strong><strong>Area \: of \: Octagonal \: surface \: =}$

$\sf \red { Ar. \: of \: ABGH + Ar. \: of \: BCFG + Ar. \: of \: CDEF}$

$= (32 + 55 + 32)m {}^{2} = 119m {}^{2}$

$\sf \blue {Hence \: Answer is \: 119m {}^{2} }$

$\bf\underline\red{Hope \: It \: Helps \: You!}$

Answer 2

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