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BEAUTY HOLIDAY UK One angle is 90⁰ (right angle) Hence, 90 + A + B = 180⁰ (angle sum of triangle) → A + B = 90⁰  The area of right angled triangle is: Area = ½ x h x b  Perimeter = the sum of the length of the sides Example: Find the area of triangle if b = 15 cm and h = 20 cm Area = ½ x b x h = ½ x 20 cm x 15 cm = 300 cm2 Pythagoras’ theorem Equilateral triangles:  All sides are equal  All angles are equal = 60⁰ Example: Find the area and perimeter of the following equilateral triangle Isosceles triangles:  Two lines are equal and  Two angles (base angles) are equal Scalene triangles:  All sides are different  All angles are different Squares Example: Consider the figure below: Find the value of X and perimeter of the rectangle. Area of rectangle = L x B 55 cm2 = 5 cm x X X = 55 cm2/5 cm = 11 cm Perimeter = 2(L + B) = 2(11 + 5) = 32 cm Example: Consider the figure below: Trapezium  One pair of opposite sides is parallel but not equal.  The area of trapezium = ½ x h x (a + b)  The perimeter of trapezium = a + b + c + h Example: Find the area of the following trapezium Area = ½ x h x (a + b) = ½ x 8 x (6 + 14) = 4 x 20 = 80 cm2 Rhombus  All sides are equal (like a distorted square).  Opposite sides are parallel.  Opposite angles are equal.  The diagonals bisect each other at 90⁰.  The diagonals bisect the angles.  All sides are equal (like a distorted square).  Opposite sides are parallel.  Opposite angles are equal.  The diagonals bisect each other at 90⁰.  The diagonals bisect the angles. Parallelogram  Two pairs of adjacent sides are equal.  Diagonals cross each other at 90⁰. i) Multi sided shapes Cycles A circle has a centre and a radius, r.  Area of a circle = πr2 (r = radius, π = 22/7 or 3.14)  Circumference of a circle = 2πr  Diameter, d = 2r Example: If AB = 30 cm AP = 15 cm = BP (perpendicular bisector)  Tangent and radius meet each other at 90⁰. Example: Consider the diagram below: Example: In the figure above if angle A = 35⁰, find the angle C. Angle B = 90⁰ (angle in semicircle) A + B + C = 180 (angle sum of triangle) 35 + 90 + C = 180 125 + C = 180 C = 180 – 125 C = 55⁰