Area (Trapezium)

Class:- Basic 6

Subject:- Mathematics

Week:- 5

Topic:  Area (Trapezium)

Behavioral objective:- At the end of the lesson the pupils should be able to:-

1. Define and draw a trapezium
2. Measure the area of a trapezium

Instructional material/Reference material:- online resources, scheme of work 

Building Background /connection to prior knowledge : Students are familiar with the ways of measurement

Content

Trapezium

A trapezium is a rectangular shape joined with either a triangle at one end or a triangle each at two ends

.ABCD is a rectangle. BCE is a triangle

.∴ ABCD + BCF = ABED

.ABED is known as a trapezium

, that is a rectangle plus a triangle as shown in Fig 1

  ABC is a triangle. EDF is also a triangle. BEDC is a rectangle

.Thus ABC + BEDC + EDF = trapezium ABEF

Hence trapezium ABEF  = a rectangle + 2 triangles as shown in Fig 2

Examples

Study these methods to find the area of parallelogram ABED in Fig 1 above given that AB = 10cm,

CE = 7cm and

AD = 4cm.Method 1

Area of rectangle ABCD = length × breadth= 10cm × 4cm = 40cm2.

Area of triangle BCD = 1/2 base height 2 × = 1 7cm 4 cm 2× × = 14cm2

Area of trapezium ABED = area of rectangle ABCD + area of triangle BCE = 40cm2 + 14cm2 = 54cm2

Method 2

Draw a line from B to D.Trapezium ABED = Triangle ABD + Triangle BED ∴ Area of ABED = Area of ABD + Area of BED Note: Area of trapezium ABED. = 1 4 cm (10 cm + 17 cm) 2 × = 1 BC (AB + DE) 2 × × = 1 height (sum of the parallel sides) 2 × × = 1 base height 2  base height 2 1 × × = 1 AB AD + 2 DE BC 2 1 × × = 1 10 cm 4 cm + 2 (10 cm + 7 cm) 4 cm

= 1 4 cm (10 cm + 17 cm) 2 = 1 4cm + 27 cm = 54cm2Examples

Study these methods to find the area of trapezium ABEF, shown in fig 2 above.

Method 1

Area of trapezium ABEF = Area of triangle ABC + Area of rectangle BEBC + area of triangle EDF = 1 base height + length breadth + 2 base height = 1 7 cm 4cm + 10 cm 4 cm + 2 4 cm 4 cm= 14cm2 + 40cm2 + 8cm2 = 62cm

Method 2Area of ABEF = 1 height sum of the parallel sides) 2 × × (= 1 BC (BE + AF) 2 × ×= 1 4 cm (10 cm + 21 cm) 2 × ×= 1 4 cm 31 cmv= 62cm2In general the area of a trapezium =

1/2(a + b)hWhere a and b are parallel lines and h is the perpendicular height.

Evaluation:- 1. A trapezium has an area of 126cm2.

If the sum of the parallel sides is 28cm,

what is the height of the trapezium?