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**Welcome to Class !!**

*We are eager to have you join us !!*

*In today’s Mathematics class, We will be talking about Area of Plane Figures. We hope you enjoy the class!*

**Area of Plane Figures**

**Area of Triangle **

$SinA=\frac{h}{c}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}h=c\times SinA\phantom{\rule{0ex}{0ex}}Areaof\u2206ABC=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.bcSinA$

**Example 1:**

Find the area of triangle PQR if sides PQ = 6cm, PR = 8cm and QR = 10cm

**Solution**

First, we need to show that ∆PQR is a right angled triangle

PQ^{2} + PR2 = QR2

6^{2} + 8^{2} = 10^{2}

36 + 64 = 100

Area of ∆PQR = $\frac{1}{2}\times 8\times 6$= 24cm^{2}

**Example 2:**

Calculate the area of triangle PQR correct to 3 significant figures if p = 8.5cm, q = 6.8cm and R = 65.4^{0}

#### Parallelogram

**Area of parallelogram = base x height = bh**

Consider the parallelogram

In general,

Area of parallelogram = product of adjacent sides x the size of the angle between the two sides

**Example 3**

Find the area of a parallelogram with base 12cm and height 7cm

**Solution**

Area of parallelogram = base x height

= 12cm x 7cm

= 84cm^{2}

**Example 4:**

Find the area of parallelogram shown in the diagram below

#### Rhombus

**Area of Rhombus = base x height = bh**

OR Area of Rhombus = $\frac{1}{2}$ of the product of diagonals

#### Trapezium

Area of Trapezium = $\frac{1}{2}(Base+Top)Height=\frac{1}{2}\left(AB+DC\right)h$

**Example 3:**

Find the area of trapezium ABCD shown below if AB = 8cm, BC = 6cm, DC = 12cm and angle BCD = 43^{0}

**Solution:**

Area of trapezium ABCD = $\frac{1}{2}\times \left(AB+DC\right)h$

Sin 43^{0} = h/6

h = 6 x sin 430

= 6 x 0.6821 = 4.092

Area of ABCD = ½ (8 + 12) x 4.092

= ½ x 20 x 4.0920 = 40.92cm^{2}

**READING ASSIGNMENT**

Essential Mathematics page 220

Ex 21.5 ; 1 – 23

**WEEKEND ASSIGNMENT**

- The area of a parallelogram is given as 108cm
^{2}. F he height of the parallelogram is 9cm, find the base of the parallelogram**A.**13cm**B.**9cm**C.**12cm - Find the area of a rhombus of side 20mm and height 10kk
**A.**20mm^{2}**B.**200mm^{2}**C.**300mm^{2} - Find the area of a circle of diameter 35cm
- The area of a circle is 1386cm
^{2}. Find the diameter of the circle**A.**21cm**B.**42cm**C.**82cm - A sector of a circle of radius 8cm has an area of 120
^{0}at the centre. Find its perimeter**A.**33**B.**34**C.**36

THEORY

- A circle has an area of 144. Calculate the circumference of the circle, leaving your answer in terms of
- Calculate the area of an annulus, which has an external diameter of 25cm and internal diameter of 15cm.

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