Perimeter

Finding the perimeter of polygons and rectilinear (L-shaped) figures, including missing side lengths.

Adding the sides

Perimeter is the total length of all the sides. For a rectangle, $P = 2l + 2w$. For a square, $P = 4s$.

Drag the corner of a rectangle

Imagine a rectangle from the origin to point C. Different rectangles can have the same perimeter but different areas.

Rectilinear shapes

A rectilinear shape has only right angles, like an L shape. To find missing sides, use the fact that the total horizontal lengths on the top equal those on the bottom (and the same for vertical).

Example 1●●

An L shape is $10$ m wide at the bottom and $8$ m tall on the left. The top edge is $4$ m and the right edge is $3$ m. Find the perimeter.

Missing horizontal: $10 - 4 = 6$ m. Missing vertical: $8 - 3 = 5$ m.

$P = 10 + 8 + 4 + 5 + 6 + 3 = 36$ m

Flashcards

Perimeter of a rectangle

$P = 2l + 2w$

Perimeter of a square, side 7

$28$

Regular hexagon, side 5

$P = 30$

Practice

Find the perimeter of the L shape in Example 1, in metres.
Find the perimeter of a square with side $7$ cm.
Find the perimeter of a regular hexagon with side $5$ m.
Find the perimeter of a $12$ cm by $5$ cm rectangle.
A rectangle has perimeter $30$ m and length $6$ m. Find its width.
A square has perimeter $48$ cm. Find its side length.
A triangle has sides $5$ cm, $7$ cm and $9$ cm. Find its perimeter.
Fencing costs $\$8$ per metre. Find the cost to fence a $12$ m by $8$ m yard (dollars).