How do I find the lengths of diagonals of an isosceles trapezoid?

Answer 1

An isosceles trapezoid can be looked at as though it were a rectangle with two congruent triangles stuck on each side. I would actually take a piece of paper and draw it out. Next label all the sides with any dimensions that you've been given.
If you know the height of the trapezoid and the length of the short side, then you know the length and height of the rectangle. Since this is a rectangle, the angles are all 90 degrees. Fortunately this means you're working with right triangles and can use a^2 +b^2 = c^2 (The Pythagorean Theorem) to solve for the lengths of the diagonals of the rectangle (which are the same as the diagonals for the trapezoid).
If you don't know the height of the rectangle, then you will have to find it first by using one of the little triangles on the side of the rectangle. Here again you will have a right triangle, so you can use the Pythagorean Theorem to find the lengths of all the sides. Fortunately one of those lengths will be the height of the rectangle and you can use this as already stated.
If you don't know the length of the top of the trapezoid, then you will have to have been given the length of the base or you won't be able to solve this problem. If you have the length of the base, figure the length of the side of one of the adjoining triangles, then subtract twice that (one for each of the triangles) from the base of the trapezoid and voila! you now have enough information to solve as originally described. Good Luck.