Question

A farm covers land in the shape of a trapezium. The length of the northern boundary of the farm is 265 m and length of the southern boundary is 180 m. The perpendicular distance from the northern end to the southern end is 90 m.

a Draw a diagram of the farm and find its area to the nearest square metre.
b Write your answer to part a to the nearest hectare.
c The farmer decides to purchase his neighbour's farm, which is in the shape of a rectangle but has the same area as his farm. What are possible dimensions neighbour's farm? Give your answer in metres.

Answer 1

Explanation:

Part A

Givens

b1 = 265

b2 = 180

h = 90

Formula

Area = (b1 + b2)*h / 2

Solution

Area = (265 + 180) * 90 / 2

Area = 445 * 90 / 2

Area = 40050 / 2

Area = 20025 square meters

Part B

1 hectare = 10000 square meters

x hectare = 20025 square meters Cross multiply

x * 10000 = 20025 * 1 Divide by 10000

x = 20025 / 10000

x = 2.0025

Rounded to the nearest hectare that would be 2

Part C

The best shape is a square.

That would mean that the area is given by

s^2 = 20025

sqrt(s^2) = sqrt(20025)

s = 141.51

Each side of the rectangle (square) = 141.51