Answer:
(1) 92.92 unit (2) 500 unit²
Step-by-step explanation:
(1) Perimeter of the given hexagon ABCDEF will be
= Sum of length of all sides
= AB + BC + CD + DE + EF + FA
=\(10+(\sqrt{10^{2}+10^{2}})+\sqrt{10^{2}+10^{2}}+10+\sqrt{20^{2}+10^{2}}+\sqrt{20^{2} +10^{2} }\)
= \(20+10\sqrt{2} +10\sqrt{2}+10+10\sqrt{(2+1)}+10\sqrt{(2+1)}\)
= \((30+20\sqrt{2}+20\sqrt{3})\)
= 30 + 28.28 + 34.64
= 92.92 unit
(2) Area of hexagon = Area of ΔAEF + Area of rectangle ABDE + Area of ΔBCD
= \(\frac{1}{2} (20)(20)+(20)(10)+\frac{1}{2}(20)(10)\)
= 200 + 200 + 100
= 500 unit²
