18. Farmer Brown has built a new barn, on horizontal ground, on his farm. The barn has a cuboid base and a triangular prism roof, as shown in the diagram. B D 15 16 diagram not to scale 1 L K 10 The cuboid has a width of 10 m, a length of 16 m and a height of 5 m. The roof has two sloping faces and two vertical and identical sides, ADE and GLF. The face DEFL slopes at an angle of 15 to the horizontal and ED = 7 m. 18a. [3 marks] Calculate the area of triangle EAD. 18b. [3 marks] Calculate the total volume of the barn. 18c. [2 marks] The roof was built using metal supports. Each support is made from five lengths of metal AE, ED, AD, EM and MN, and the design is shown in the following diagram. A E M 10 r ED=7 m, AD = 10 m and angle ADE = 15. M is the midpoint of AD. N is the point on ED such that MN is at right angles to ED. Calculate the length of MN. 18d. [3 marks] Calculate the length of AE. 18e. [3 marks] Farmer Brown believes that N is the midpoint of ED. Show that Farmer Brown is incorrect. 18f. [4 marks] Calculate the total length of metal required for one support. diagram not to scale 15