Lin and Andre used different methods to find the area of a regular hexagon with 6-inch sides. Lin decomposed the hexagon into six identical triangles.
Andre decomposed the hexagon into a rectangle and two triangles.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

On a cm grid, point p has coordinates (3,-1) and point q has coordinates (-5,6) calculate the shortest distance between p and q give your answer to 1 decimal place

The given diagram shows the parts of a right triangle with an altitude to the hypotenuse. using the two given  measures, find the other four.