Question

An ant is moving around a few food pieces of different shapes scattered on the floor. For which food piece would the ant have to take a longer round?

Answer 1

a) Radius $=\frac{2.8}{2}=1.4cm$

Perimeter of figure (a) $=$ length of diamter + Circumference of the semicircle

$=2R+\pi R=2.8+\frac{22}{7}\times 1.4=7.2cm$

b) Radius $=\frac{2.8}{2}=1.4cm$

Perimeter of figure (b) $=$ 2 times length of 1.5 cm + 2 times radius + circumference of semicircle

$=1.5\times 2+2R+\pi R=3+2.8+\frac{22}{7}\times 1.4=5.8+\frac{22}{7}\times 1.4=10.2cm$

c) Radius $=\frac{2.8}{2}=1.4cm$

Perimeter of figure (c) $=$ Circumference of semicircle + 2 times length 2 cm

$=2\times 2+\pi R=4+\frac{22}{7}\times 1.4=8.4cm$

So, figure (b) has largest perimeter.

Hence, for food piece (b), the ant would have to take a longer round.