A large plot of land is shaped like a trapezoid, ABCD, where AB is parallel to CD, AB = 12 km and CD = 8 km. The diagonal BD of the trapezoid is equal to 10 km. The internal angle ABD is equal to 58º. D 8 km С
D 10 km B
Angle B is 58
А 12 km B
Let a new point, H, be a point on AB closest to D.

(a) Calculate the distance from H to D.
(b) Calculate the length of AD.
(c) Calculate the size of the angle DÂB. A landowner estimates that the length of AD is equal to 11.5 km.
(d) Calculate the percentage error in the landowner's estimate.

The landowner decides to install cone-shaped concrete bollards along the perimeter of the plot of land. The bollards are to be installed at a distance of 100 m from each other. The radius of the base of each bollard is 20 cm and the height of each bollard is 40 cm.

(e) Calculate the volume of one of the bollards. (f) Calculate the total volume of concrete needed to install all the bollards.​