# 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:-**

**Define and draw a trapezium****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 **

**Conten****t**

**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 = 40cm****2.**

**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 = 54cm2****Examples**

**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 2****Area 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 cm****v****= 62cm2****In general the area of a trapezium = **

**1****/****2(a + b)h****Where 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?**** **

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