Rhombus ABCD has vertices (1, 10), (-4, 0), (7, 2), (12, 12), respectively. Part 1

Use the distance formula to find the lengths of the diagonals.

Part 2

Use the lengths of the diagonals to calculate the area of the rhombus.

Part 3

One of the similar characteristics in a square and rhombus is that they both have four equal sides. The formula for the area of a square uses the side lengths to compute the area while the formula for the area of a rhombus uses the lengths of the diagonals to compute the area. Are area formulas for a square and rhombus interchangeable? In complete sentences, explain why or why not you think that the formulas are interchangeable. Create your own example using a square with side lengths and a rhombus with side lengths to prove your explanation.

Complete your work in the space provided or upload a file that can display math symbols if your work requires it. If necessary, round your answers to the nearest tenth of a unit.