Area, Perimeter and Symmetry

Stage 5 of 23 Strand 6 of 9 4 lessons

4 illustrated lessons, each teaching the why before the how.

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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.

Now you

Area of a 5 by 3 rectangle

Area of a 5 by 4 rectangle

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.

Now you

A rectangle has area 21 cm² and one side 3 cm. The other side?

A square has area 64 cm². How long is each side?

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.

Now you

How many lines of symmetry?

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.

Now you

The figure’s open corner reflects to which dot?