A plane shape is a two-dimensional figure. It is a closed flat figure that has only length and breadth.

A side (or edge) is a straight line that makes part of a shape.

A corner (or vertex) is a point where two sides meet.

A diagonal is a straight line joining one vertex to the opposite vertex.

The perimeter is the total distance round a plane shape. It is the sum of all the sides.

The area is the amount of surface enclosed within a plane shape. It is measured in square units.

Square

+------+
|      |
|      |
+------+
  

Four equal sides, four right angles, opposite sides parallel, diagonals equal and bisect at right angles, four lines of symmetry.

Rectangle

+----------+
|          |
|          |
+----------+
  

Four sides, opposite sides equal and parallel, four right angles, diagonals equal and bisect each other, two lines of symmetry.

Parallelogram

  /------/
 /      /
/------/
  

Opposite sides parallel and equal, opposite angles equal, diagonals bisect each other.

Rhombus

   /\
  /  \
  \  /
   \/
  

A parallelogram with four equal sides, diagonals meet at right angles.

Trapezium

  +------+
 /        \
+----------+
  

A quadrilateral with one pair of parallel sides.

Kite

  /\
 /  \
 \  /
  \/
  

A quadrilateral with two pairs of adjacent equal sides, one line of symmetry.

Triangle

   /\
  /  \
 /____\
  

A polygon with three sides and three angles, sum of interior angles is 180°.

Circle

   ****
 *      *
*        *
 *      *
   ****
  

The set of all points at a fixed distance called the radius from a centre, no sides or corners, circumference is its perimeter.

1. All the shapes are plane or flat closed figures.


2. Square, rectangle, parallelogram and trapezium are all quadrilaterals.


3. Triangle, square, rectangle, trapezium and parallelogram are polygons because they have straight sides, while a circle is not a polygon.


4. Square and rectangle both have four right angles and equal diagonals.


5. Square, rectangle, parallelogram and trapezium all have at least one pair of parallel sides.


6. Circle, square and rectangle all have symmetry.

DIFFERENCES BETWEEN PLANE SHAPES (COMPARISON)

Number of sides

1. Square has four sides.


2. Rectangle has four sides.


3. Triangle has three sides.


4. Trapezium has four sides.


5. Parallelogram has four sides.


6. Circle has no sides.

Angles

1. Square has four right angles.


2. Rectangle has four right angles.


3. Triangle has three angles and the sum is 180 degrees.


4. Trapezium has no fixed angles.


5. Parallelogram has opposite angles equal but not necessarily right.


6. Circle has no angles.

Parallel sides

1. Square has two pairs of parallel sides.


2. Rectangle has two pairs of parallel sides.


3. Triangle has no parallel sides.


4. Trapezium has one pair of parallel sides.


5. Parallelogram has two pairs of parallel sides.


6. Circle has no sides so no parallel sides.

Equal sides

1. Square has all four sides equal.


2. Rectangle has opposite sides equal.


3. Triangle may have all sides equal (equilateral), two equal sides (isosceles), or no equal sides (scalene).


4. Trapezium does not have all sides equal except in special cases.


5. Parallelogram has opposite sides equal.


6. Circle has equal radius from the centre but no straight sides.

Diagonals

1. Square has diagonals equal and they bisect at right angles.


2. Rectangle has diagonals equal and bisect each other.


3. Triangle has no diagonals.


4. Trapezium diagonals are not equal except in isosceles trapezium.


5. Parallelogram has diagonals that bisect each other but are not equal.


6. Circle has no diagonals.

Symmetry

1. Square has four lines of symmetry.


2. Rectangle has two lines of symmetry.


3. Triangle symmetry depends on type. Equilateral has three lines, isosceles has one line, scalene has none.


4. Trapezium usually has none, except isosceles trapezium which has one line.


5. Parallelogram has no line symmetry but has rotational symmetry of order two.


6. Circle has infinite lines of symmetry.

FORMULAE

Rectangle: Perimeter P = 2(l + b), Area A = l × b.

Square: Perimeter P = 4s, Area A = s × s = s².

Triangle: Perimeter P = a + b + c, Area A = ½ × base × height.

Parallelogram: Perimeter P = 2(a + b), Area A = base × height.

Trapezium: Perimeter P = a + b + c + d, Area A = ½ (a + b) × height.

Circle: Circumference C = 2πr or πd, Area A = πr².

WORKED EXAMPLES

Example 1: Perimeter of a rectangle

A field measures 80 metres by 50 metres. Find its perimeter.

P = 2(L + b)
  = 2(80 + 50)
  = 2 × 130
  = 260 metres.
Answer: 260 metres.
  

Example 2: Area of a rectangle

Length = 12 metres, breadth = 8 metres.

A = l × b
  = 12 × 8
  = 96 square metres.
Answer: 96 m².
  

Example 3: Perimeter of a square

Side = 15 cm.

P = 4s
  = 4 × 15
  = 60 cm.
Answer: 60 cm.
  

Example 4: Area of a square

Side = 6 cm.

A = s²
  = 6 × 6
  = 36 cm².
Answer: 36 cm².
  

Example 5: Perimeter of a triangle

Sides are 13 cm, 14 cm and 15 cm.

P = 13 + 14 + 15
  = 42 cm.
Answer: 42 cm.
  

Example 6: Area of a triangle

Base = 10 cm, height = 6 cm.

A = ½ × base × height
  = ½ × 10 × 6
  = 30 cm².
Answer: 30 cm².
  

Example 7: Circumference of a circle

Radius = 7/2 metres = 3.5 m. Use π = 22/7.

C = 2 × 22/7 × 7/2
  = 22 m.
Answer: 22 metres.
  

Example 8: Perimeter of a trapezium

Sides = 8 cm, 5 cm, 8 cm, 7 cm.

P = 8 + 5 + 8 + 7
  = 28 cm.
Answer: 28 cm.
  

SUMMARY

Plane shapes are flat closed figures with only length and breadth. Examples are square, rectangle, triangle, trapezium, parallelogram and circle. They have similarities such as being closed figures, while they differ in sides, angles, diagonals, parallel sides and symmetry. Each shape has specific formulae for perimeter and area. Problems must be solved step by step using the correct formula.