The Field An Investigation

The Field The drawing (which is NOT drawn to scale) shows a field. The area of the field is 8000 square metres. The field is in the shape of a trapezium. The wider end is 82 metres long, and the narrower end is 54 metres long. The dotted line is a fence which divides the field into two parts which are equal in area. How far is the fence from the wide end? Give your answer to the nearest metre. fence 54m 82m

Exercise If the field was to be divided into three equal parts using two parallel fences, where would these fences need to be placed in the field?

Solution Length of baseline = m Let x be length from 82m side to fence and h the length of the fence. Obtain from the left part and from the other part. Putting these equal leads to the quadratic equation 28x 2 – x = 0, which solves to give x = This gives h = 69.43