A square, whose side is 2m, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres, is

A ladder leans against a vertical wall. The top of the ladder is $8 \mathrm{m}$ above the ground. When the bottom of the ladder is moved $2 \mathrm{m}$ farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?

Two sides of a plot measure $32 \mathrm{m}$ and $24 \mathrm{m}$ and the angle between them is a perfect right angle. The other two sides measure $25 \mathrm{m}$ each and the other three angles are not right angles.

What is the area of the plot?

In $∆\mathrm{DEF}$ shown below, points $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are taken on $\mathrm{DE}, \mathrm{DF}$ and $\mathrm{EF}$ respectively such that $\mathrm{EC}=\mathrm{AC}$ and $\mathrm{CF}=\mathrm{BC}.$ If $\angle \mathrm{D}=40°,$ then $\angle \mathrm{ACB}=$

In the figure, $\mathrm{AB}=\mathrm{BC}=\mathrm{CD}=\mathrm{DE}=\mathrm{EF}=\mathrm{FG}=\mathrm{GA}.$ Then $\angle \mathrm{DAE}$ is approximately