**TERM: 2nd TERM**

**SUBJECT: ****BASIC TECHNOLOGY **** **** **** **** **** **** **

**CLASS: JSS 2**

**REFERENCE MATERIALS **

- MELROSE, Basic Science and Technology, Book 2
- NERDC, Basic Technology for JSS, Book 2

**WEEK FOUR AND FIVE**** **

**TOPIC**: **AREA OF PLANE FIGURE**

**INTTRODUCTION**

Plane figures are flat two-dimensional shapes. The can be made of straight lines, curved lines or both straight and curved lines. Examples of plane figures are: triangle, square, parallelogram, circle, rectangle etc.

**AREA OF PLANE FIGURES**

When a plane figure is drawn, it occupies a certain amount of space. At times, it is important to know the amount of space of a figure occupies, when it is drawn. This way, it will be possible to draw a different shape that has the same amount of space with it.

Therefore, area of a plane figure can be defined as the space it occupies.

**Area of a triangle**

Area = ½ of (b x h) where b=base and h= vertical height

**Note: **The area of any plane figure (polygon) can be reduced to a combination of areas of rectangles (Or squares) and triangles each of which can be computed and the total area together.

**Area of a rectangle**

Area= l x b where l= length and b= breadth

**Area of a square**

Area= a x a= a2 where a= length of side

**Area of a parallelogram **

Area= b x h where b= base and h= vertical height

**Area of a circle**

Area= πr2 where r= radius

**Evaluation **

- Define the area of plane shape.
- State the area of (i) triangle (ii) rectangle

**THEOREMS **

In construction regular plane figure of equal areas, some geometrical laws, generally called theorems, are applied. For instance, the following are will be relevant to this topic:

**Triangles on the same base and between the same parallels are equal in area.****Triangles on equal bases and between the same parallels are equal in area.****Parallelograms on the same base and between the same parallels are equal in area.****Parallelograms on equal base and between the same parallel are equal in area.****A triangle on the same parallels with a parallelogram is half the area of the parallelogram.****If a triangle and a parallelogram are on equal bases and between the same parallels, the triangle is half the area of the parallelogram**

**Evaluation **

- State 6 theorems of area of plane shape
- Sketch diagrams that demonstrate the theorems of plane shape.

**CONSTRUCTION OF SIMILAR AREA OF PLANE SHAPES**

**Constructing a triangle equal in area to a given rectangle**

**Procedure **

- Draw the rectangle ABCD
- Project line CD and mark off DE, using the distance equal to CD.
- Draw a horizontal line from point F to line BA parallel to BC.
- Locate point G anywhere on line EF.
- Join point G to B and C respectively, to obtain the triangle equal in area to rectangle ABCD. Triangle BCG is equal to the given rectangle.

**Constructing a rectangle equal in area to a given triangle **

**Procedure **

- Draw the given triangle ABC.
- Draw a line through A, parallel to BC.
- Bisect line BC perpendicular at D and to meet the line through at D and to meet the line through A at E.
- Draw a perpendicular to BC at B meet the line through A at F.
- FBDE is the rectangle required

**Evaluation **

- Construct a triangle equal in area to a rectangle AB=50mm, BC=60mm.
- Construct a rectangle equal in area to a triangle ABC, AB= 40mm, AC=70mm and BC=60mm

**Constructing a triangle equal in area to any regular polygon **

**Procedure**

- Draw the regular polygon (hexagon) ABCDEFG
- Draw the diagonals to intersect at the centre of the polygon O.
- Draw HI equal in length to the length of side x number of sides. In this exercise, GH is equal to six times, the length of the side of the hexagon. (HI= 6 x y mm)
- Join O to G and H, GOH is required triangle

**Constructing a triangle equal in area to a given circle**

**Procedure **

- Draw the given circle of diameter AB and centre O.
- Divide the radius OA into 7 equal parts
- Draw a perpendicular line at A equal in length to 3 1/7
- Join C to B.ACB is the required triangle

**Reducing an irregular quadrilateral to half its original area**

**Procedure **

- Draw the given irregular quadrilateral ABCD
- Draw a diagonal BD
- Bisect AB perpendicular at E
- With centre E and radius EA, draw an arc to meet the bisector at F.
- With centre B and radius BF, draw an arc, which meets the bisector at F.
- From G and GH parallel to AD, also draw HI parallel to DC.
- GBIH is required reduced irregular quadrilateral.

**Evaluation**

- Construct a triangle equal in area to any regular hexagon 50mm.
- Draw a triangle equal in area to a given circle of radius 40mm.

**READING ASSIGNMENT**

Read more about AREA OF PLANE FIGURES

**REFERENCE MATERIALS **

- MELROSE BASIC SCIENCEBASIC TECHNOLOGY BOOK 2, page 86-92
- NERDC- BASIC TECHNOLOGY BOOK 2, page 61-63

**WEEKEND ASSIGNMENT **** **

- The space which a plane shape occupies is known as _______ A. triangle B. rectangle C. parallelogram D. area
- The units of area are as follows except A. mm2 B. cm2 C. kg2 D. m2
- Triangles on the same base and between the same parallels are equal in area A. True B. False C. None of the above D. All of the above
- A triangle on the same base and between the same parallels with a parallelogram. A. True B. False C. None of the above D. All of the above
- The area of a triangle is ____A. ½ B x H B. B x H C. B2 x H D. B x H2

**THEORY **

- State 6 theorems of area of plane shape
- Construct a right-angled triangle, which has the same area with an equilateral triangle of side 60mm.

© Lesson Notes All Rights Reserved 2023