Question

6. Find the area of an octagon ABCDEFGH having each side equal
to 5 cm, HC = 11 cm and AP 1 HC such that AP = 4 cm.​

Answer 1

Step-by-step explanation:

to find Area of a octagon divide it in to 8 triangles .

Now let one triangle have base a vertex angle k . then there are such 8 angles . so 8k = 2π or

k=2π/8 = π/4 .

Note that

$k = 2 \alpha \implies \: \alpha = \frac{k}{2} = \frac{\pi}{8}$

$\tan( \alpha ) = \frac{ \frac{a}{2} }{h} \\ \implies \: h = \frac{5}{2 }{\cot( \alpha ) } = \frac{5}{2} \cot( \frac{\pi}{8} ) = 6.03$

Now area of small triangle

∆ = 1/2bh = 1/2× 5 × 6.03 = 15.075 cm2

So total area = 8 × 15.075 = 120.6 cm2