6.26: For equilateral triangles, as long as the side length is known, the height can be calculated the same way.  Remember the height splits the equilateral triangle into two $30$-$60$-$90$ triangles.

6.30: The corner is a $45$-$45$-$90$ triangle.  The side length ratio of such a triangle is $1:1:\sqrt{2}$.  If teh hypotenuse is $x$, it means $x$ corresponds to the $\sqrt{2}$ part, so the leg length is $\dfrac{x}{\sqrt{2}}$.

6.24: An interior angle of a regular octagon is $135^\circ$.

6.22: You can calculate all the angles of the quadrilateral.