CHAPTER 23

Quadrilaterals

Special Quadrilaterals1. Square

a) All sides are the same length

b) All angles are the same size (90°)

c) Its diagonals bisect each other at right angles

d) Its diagonals are equal on length

e) It has 2 pairs of parallel sides

2. Rectangle

a) The opposite sides are equal in length

b) All angles are the same size (90°)

c) Its diagonals are equal in length

d) It has 2 pairs of parallel sides

e) Its diagonals bisect each other

Special Quadrilaterals3. Rhombus

a) All sides are the same length

b) Opposite angles are equal

c) Its diagonals bisect each other at right angles

d) It has 2 pairs of parallel sides

4. Parallelogram

a) The opposite sides are equal in length

b) Opposite angles are equal

c) It has 2 pairs of parallel sides

d) It diagonals bisect each other

Special Quadrilaterals5. Kite

a) Its diagonals bisect each other at right angles

b) Two pairs of adjacent sides equal

c) One pair of opposite angles are equal

6. Trapezium

a) One pair of parallel sides

b) It has no axes of symmetry

7. Isosceles Trapezium

a) One pair of parallel sides

b) Non parallel sides equal

c) Two pairs of equal angles

d) Its diagonals are equal in length

Sum of the angles of a Quadrilateral

The sum of the interior angles of any quadrilateral is 360°.

Symmetry of Special Quadrilaterals

1. Squarea) It has 4 lines of symmetryb) order of rotational symmetry = 4

2. Rectanglea) It has 2 lines of symmetryb) order of rotational symmetry = 2

Symmetry of Special Quadrilaterals3. Rhombusa) It has no axes of symmetryb) No rotational symmetry

4. Parallelograma) It has no axes of symmetryb) No rotational symmetry

5. Kitea) It has one axis of symmetryb) No rotational symmetry

Symmetry of Special Quadrilaterals6. Trapeziuma) It has no axes of symmetryb) No rotational symmetry

7. Isosceles Trapeziuma) One axis of symmetryb) No rotational symmetry

Perimeter of QuadrilateralsThe PERIMETER of a quadrilateral is the total length of its 4 sides.

Area of Special Quadrilaterals1. Rectangle

Area = Length x Breadth

A = lb

2. Square

Area = Length x Breadth

In a square, Breadth = Length

Area = Length x Length

Area = Length2

A = l2

Length, l

Breadth, b

Length, l

Symmetry of Special Quadrilaterals3. Rhombus

Area = Base x Height

A = bh

4. Parallelogram

Area = Base x Height

A = bh

Base, b

Height, h

Base, b

Height, h

Area of Special Quadrilaterals5. Trapezium

Area = ½ x sum of parallel sides x perpendicular height

A = ½(a + b)h

6. Kite

Area = sum of the areas of the 2 triangles

Height, h

a

b

Area of a Triangle The area of a TRIANGLE is calculated using the formula:

Area = ½ x base x perpendicular height

this is sometimes written as:

Area = base x perpendicular height

2

A = ½ x b x h

A = ½ x 8 x 6

A = ½ x 48

A = 24cm2

8cm

6cm