KA-0013Perimeter and area of rectilinear shapes
3 points, difficulty 1 of 3Level 3–4about 45sThe L-shaped figure is made of unit squares. What is its perimeter?
Text description of the figure
An L-shaped figure made of unit squares: a vertical column 3 squares tall and 1 square wide, with 2 extra squares attached along the bottom to the right, so the shape covers 5 unit squares in total.
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Walk right around the outline, counting unit edges.
2The strategy
Perimeter is the total length of the boundary, so trace the outside of the shape and count how many unit edges you cross, including the two edges at the step.
3The full solution
Walk round the outline from the bottom-left corner: 3 up, 1 right, 2 down, 2 right, 1 down, 3 left. That is 3 + 1 + 2 + 2 + 1 + 3 = 12 unit edges.
Solution— no shortcut on this one
Trace the boundary once, counting unit edges as you go. Starting at the bottom-left corner and going up the tall side: 3 up, 1 right, 2 down, 2 right, 1 down, 3 left back to the start. That is 3 + 1 + 2 + 2 + 1 + 3 = 12 unit edges, so the perimeter is 12. The transferable idea: trace the outline once and count edges, rather than adding rectangle perimeters.
Why this is on the test: Perimeter and area get confused constantly, and rectilinear shapes with a step are where that confusion shows up on the paper.