What is the height of the trapezoid?

Question

It's an isosceles trapezoid, the top base equals 30, the bottom base equal 70 and the side equal 29.

Answer 1

We can imagine the trapezoid as made up of two congruent right triangles attached to each end of a rectangle.

If the height is h, then the rectangle has base length 30 and height h.

The bases of the two right triangles equally share the difference between the lengths of the two trapezoid bases=70-30=40, so the triangle base is 40/2=20. We have the base=20 and hypotenuse=29, so, by Pythagoras: 29²=20²+h², h²=(29-20)(29+20)=9×49=3²×7²,  making h=3×7=21 units.