Question

A) Calculate the area enclosed if the fence is in the shape of

i) a square. ii) a circle.
iii) a rectangle with a length that is three times its width.
Give each answer to the nearest integer.
b) Which of these three shapes maximises the enclosed area?

Answer 1

a)i. A = (240/4)² = 60² = 3,600 m²

ii. 2πr = 240

r = 120/π

A = π(120/π)² = 14,400/π

= about 4,583 m²

iii. w + 3w = 120

4w = 120

w = 30, l = 90

A = 90(30) = 2,700 m²

b) The circle maximizes the enclosed area.