Area, Perimeter and Symmetry

Area and Perimeter #

The walk around, and the covering inside.

Perimeter is the walk around the edge, area is the covering inside

The perimeter is the total distance around a shape: 5 + 3 + 5 + 3 = 16 cm.

The area is the space enclosed: 15 centimeter squares, written 5 × 3 = 15 cm².

Cut a corner out: the walk turns in 2 and back out 2, so it is as long as before.

Finding a Missing Side #

Run the area or perimeter backwards.

Work the area or perimeter backwards and the missing side falls out

Area 24 with 4 rows: each row must hold 24 ÷ 4 = 6 squares — the width is 6.

Perimeter 26 with two sides of 5: the widths share 26 − 10 = 16, so each is 8.

A square of area 49 has equal sides: the side times itself is 49, so it is 7.

Symmetry #

When a fold lays one half on the other.

A shape is symmetrical if a fold would lay one half exactly on the other

A line of symmetry cuts a shape into two identical, matching halves.

Fold along the dashed line and both halves land right on top of each other.

This trapezium has exactly one fold that works.

A square has four: two through the edges and two along the diagonals.

Completing a Symmetric Figure #

Count to the mirror line, then count again.

Each dot’s mirror twin sits the same distance beyond the line

The dashed line is the mirror: each corner has a twin the same distance beyond.

A corner 3 gaps left of the line has its twin 3 gaps right — count, cross, count.