Giải thích các bước giải:

1.Vì $AI=IK=KH$

$\to \dfrac{AI}{AH}=\dfrac13, \dfrac{AK}{AH}=\dfrac23$

Ta có: $EF//MN//BC$

$\to \dfrac{EF}{BC}=\dfrac{AE}{AB}=\dfrac{AI}{AH}=\dfrac13$

$\to EF=\dfrac{20}3$

Ta có: $\dfrac{MN}{BC}=\dfrac{AM}{AB}=\dfrac{AK}{AH}=\dfrac23$

$\to MN=\dfrac{40}3$

2.Đổi: $0.8\: m^2=8000\: cm^2$

Ta có:

$AH=\dfrac{8000\cdot 2}{20}=800$

$\to AK=KI=IH=\dfrac13AH=\dfrac{800}3$

$\to S_{EFNM}=\dfrac12IK\cdot (EF+MN)=\dfrac12\cdot\dfrac{800}3\cdot (\dfrac{20}3+\dfrac{40}3)=\frac{8000}{3}$