TRIANGLE
1) It has 3 sides : XY, XZ, YZ
2) It has 3 angles a, b, c
3) Total interior angles = 180o
Equilateral Triangle
(a) All sides are of EQUAL LENGTH
(b) Each ANGLE = 180 / 3 = 60o
Isosceles triangle
(a) 2 sides of equal length (black lines)
(b) 2 angles are of equal degree
Right-angle triangle
(a) one of the angle is 90o
(b) The two sides that form the right angle are the base and height
Perimeter and Area of a triangle
Triangle A
Area of Triangle A = ½ x B1 x H1
= ½ x B2 x H2
= ½ x B3 x H3
Base and Height
Base can be any of the three lines of the triangle.
Height is the line that form a right angle with the base line. It can be called the perpendicular line.
Base and Height are perpendicular
How to find the height and base in a Triangle?
Example
Step 1: Choose the base (using BC)
Step 2: Find the joining point (or vertex A) from the other 2 lines (AB and AC)
Step 3: Put ruler at A, and draw a line(at right angle) to meet BC
Example
Step 1: Determine the base (using BC)
Step 2: Find the joining point (or vertex A) of the other 2 lines (AB and AC)
Step 3: Put ruler at A, and draw a line(at right angle) to meet BC (extend it)
Examples
Area of triangle = ½ x B x H
Area = ½ x 4 x 3 Area = ½ x 5 x 4 Area = ½ x 8 x 3
= 6 cm2 = 10cm2 = 12 cm2
Example
Example
In the shaded figure, ABC is a triangle with AB=BC and a height of 6cm. ABCD is a rectangle with AE = 5cm and ED = 12cm
(a) What is the area of ACDE?
(b) What is the area of the shaded figure?
(c) The perimeter of shaded figure is 36cm. What is the length of AB?
Step1: Circle/Underline Keyword. Trace/Draw what is required
< Area of ACDE, ABC and perimeter of figure)
Step2: What are the formulae for this shape?
<Area of rectangle = length x height, perimeter = 2(length + breadth)>
<Area of triangle = 1/2 x base x height), perimeter = sum of 3 sides
< Property of Isosceles triangle>
Step3: Use the formula and calculate required measurement <AB>
(a) Area of ACDE = L X B = 10 x 4
= 40cm2
(b) Area of shaded figure = Area of ACDE + Area of ABC
= 40+ (½ x 6 x 10)
= 40 + 38
= 78cm2
(c) The perimeter of the shaded figure is 42 cm.
38 = 10 + 4 + AB + BC + 4
AB = BC (isosceles triangle)
2AB = 36 – 10 – 4 – 4
2AB = 18
AB = 18/2 = 9cm
TRAPEZIUM
Trapezium is a 4-sided shape(quadrilateral) with one pair of parallel sides.
Area of trapezium = ½ (a + b) x h (height)
Formula of Trapezium
Area of Trapezium = ½ (sum of 2 parallel lengths) x height
Perimeter of Trapezium = Sum of 4 sides
Method
Example
ABCD is a trapezium. Given that AD = 4cm, AB = 3cm, DC = 5cm and BC = 6cm.
Find the area and perimeter of ABCD.
Step1 : Circle/Underline Keywords. Mark the 2 parallel sides
Step2 : Mark the height : h
Step3 : Use the formula to calculate
Area of ABCD = ½ (AD + BC) x AB
= ½ (4 + 6) x 3
= ½ x 10 x 3
= 15 cm2
Perimeter = AD + DC + BC + AB = 4 + 3+ 5 + 6 = 18 cm
More Shape Formations
(1) Draw the original shape, and help the learner discover possible new formation by:
a. ADDING
Combining shapes to form common shapes(eg: square, rectangle, triangle, trapezium)
b. SUBTRACTING
Deconstructing – taking apart the figure to form common shapes
(2) Compute required areas for the common shapes
Examples:
By ‘adding’
By ‘Subtracting’
By ‘Adding’ and ‘Subtracting’
By ‘Combining’
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