Discover Mathematics P4: Term 2, Unit 12, Lessons 1–5
GoalFind the perimeter of polygons, and find the lines of symmetry of a shape.
New words
perimeter · the distance all the way round a shape; the sum of its side lengthsregular polygon · a polygon whose sides are all equal and whose angles are all equalline of symmetry · a line that folds a shape into two halves that match exactly
Explanation
The perimeter of a polygon is the sum of all its side lengths. For a garden shaped like a house with sides 6 m, 4 m, 5 m, 5 m and 4 m, the perimeter is 6 + 4 + 5 + 5 + 4 = 24 m, the length of fence we need. If all the sides are equal (a regular polygon), multiply: perimeter = number of sides × side length. A regular hexagon with side 4 cm has perimeter 6 × 4 = 24 cm. We can work backwards: a regular pentagon with perimeter 30 cm has side 30 ÷ 5 = 6 cm. A shape has a line of symmetry if we can fold along a line and the two halves match exactly. A square has 4 lines of symmetry. A rectangle that is not a square has 2: the folds through the middles of opposite sides. Its diagonals are not lines of symmetry.
Worked examples
A garden plan is shaped like a house. Its sides are 6 m, 4 m, 5 m, 5 m and 4 m. Perimeter = 6 + 4 + 5 + 5 + 4 = 24 m. Mr Hassan needs 24 m of fence.
A regular hexagon has 6 equal sides of 4 cm. Perimeter = 6 × 4 = 24 cm. Backwards: a regular pentagon has perimeter 30 cm, so one side is 30 ÷ 5 = 6 cm. Check: 5 × 6 = 30.
Fold a square along the dashed lines: each fold makes two matching halves. A square has 4 lines of symmetry: 2 through the middles of opposite sides and 2 along the diagonals. A rectangle that is not a square has only the 2 lines through the middles of opposite sides.
Class activity
Fold and measure. Cut a square, a rectangle and a triangle with 3 equal sides from paper. Fold each one to find all its lines of symmetry and draw them. Then measure the sides with a ruler and find each perimeter. Check: the square and the triangle should have 4 and 3 lines of symmetry.
Practice
1
A rectangular garden is 9 m long and 6 m wide. Find its perimeter and its area.
Perimeter = 2 × (9 + 6) = 30 m. Area = 9 × 6 = 54 square metres.
2
A stop sign is a regular octagon with sides of 5 cm in a model. What is its perimeter?
8 × 5 = 40 cm.
3
The border of a regular hexagon tile has perimeter 42 cm. How long is one side?
42 ÷ 6 = 7 cm.
4
How many lines of symmetry does a rectangle that is not a square have?
2 lines of symmetry.
5
Aya says a diagonal of a rectangle is a line of symmetry. Is she right?
No. If we fold a rectangle along a diagonal, the two halves do not match exactly. Only a square has its diagonals as lines of symmetry.
