# Why are stop signs a hexagon

## This is math 4, workbook

63 H Theorem of Pythagoras in flat figures 2 Calculations in special polygons 3 Proofs for the Theorem of Pythagoras The opposite parallelogram has a different designation of the sides, the diagonals and the height. 1) Give formulas how one can calculate the lengths of the diagonals s and t from the given side lengths m and n and the height g! x =, s =, t = 2) Calculate the length of the diagonal if g = 3.6dm, m = 4.1dm and n = 3.9dm! t = dm From an isosceles trapezoid ABCD we know a = 15.0 cm, c = 10.2 cm and h = 3.2 cm. Calculate the leg length b = d, the diagonal length e = f and the area of ​​the trapezoid! a) First make a sketch and describe in your own words how you will proceed! b) Do the calculations! x = (a - c)  2 = cm, b = d = cm, e = f = cm, A = cm 2 A candy is placed in a special packaging. The cross-section of this packaging is trapezoidal with a base length of a = 4 cm. The parallel side c is 1.8 cm long. The packaging has a height of h = 3 cm and the length of the diagonal e of the cross-sectional area is 4.84 cm. 1) Calculate the missing side lengths and the length of the diagonal f! b = cm d = cm f = cm 2) The candy itself has a rectangular cross-section and is 1.5 cm high. How wide can the candy be so that it still fits in the pack? Solve with the help of a construction! A mirror has the shape of a regular hexagon (➞ figure). Rafael thinks that he can calculate the height and size of the mirror surface (inner hexagon) if he knows the edge length a. He says: “The regular hexagon is made up of six equilateral triangles with side length a. Using the formula for the equilateral triangle, I calculate the area and the height of one of these triangles and can then deduce the size of the mirror surface. ”Is Rafael right? Give reasons for your answer! The side edge of the adjacent stop sign is a = 25 cm long. The longest diagonal has a length of 65.3 cm. 1) Calculate the area of ​​the stop sign! A ≈ cm 2 2) The stop sign is cut out of a square plate. How many cm 2 of waste material is there at least? Enter the value in percent! Waste:% Prove the Pythagorean theorem for the special case of the right-angled isosceles triangle with the help of set triangles: Place a set square on the table top and group eight more congruent set squares as shown in the figure on the left! Carry On The Proof! 248 D A O I A x m B n m D t s g C 249 D A O I 250 D A O I h a 251 D A O I 252 D A O I 253 D A O I For testing purposes only - property of the publisher öbv