Problem of the Week
Problem B and Solution
Take A Hike!
Problem
Using your GPS app, you decide to plot your walk using the graphing option. Below is a
description of your path; all turns are right angles (90◦ ).
Walk north 100 m, then west 50 m, then south 150 m, then east 250 m, then north 100 m, then
west 150 m, then south 50 m, and finally west 50 m.
a) On the grid given below, trace your path if your journey begins at point S. Determine
the name of the resulting shape.
b) Determine the perimeter of the resulting shape.
c) Find the area enclosed by the map of your hike.
d) On graph paper, make another hike that starts and finishes at the same point. List the
direction and distance of each side to share with your classmates. With your partner,
figure out the name for the shape formed by each hike, and find its perimeter, and the
area enclosed.
Solution
a) The shape of the hike is
an irregular octagon.
b) Using the given lengths of each side, we see that the perimeter of the octagon is
100 + 50 + 150 + 250 + 100 + 150 + 50 + 50 = 900 m.
c) The area enclosed by the map of the hike is the sum of the areas of rectangles A, B, C.
Since each rectangle has area equal to its length times its width, the total area is
50 × 150 + 50 × 50 + 150 × 100 = 7 500 + 2 500 + 15 000 = 25 000 m2 .
d) Answers will vary.