Slide 1: By D. Vasu Raj, M.Sc, B.Ed.,
Minjur Panchayat Union Middle School,
Thiruvallur District, Tamil Nadu, India “THE SHAPES” WELCOME Slide 2: About this lesson plan ITLA 2009-10 2 Slide 3: OBJECTIVES ITLA 2009-10 3 Slide 4: Have you seen a floor mat ? Can you climb over it? Here is a wooden box Can you climb over it? Can you identify the difference between
these questions? PLANES AND SOLIDS 4 Slide 5: We can only sit on the mat because
it is spread flat on the floor. But We can climb on the box because it has some height. Yes this is the difference between
Plane Surface and Solids Surface has two dimensions length and Breadth Yes you are right! But solids have three dimensions
length , Breadth and height 5 Slide 6: FIND THE GEOMETRICAL SHAPES 6 Slide 7: Once again name the shapes SQUARE
PARALLELOGRAM 7. CUBE
11.CONE 7 Slide 8: MEASUREMENTS There are various type of measurements used in geometry.
Volumetric measurement. 8 Slide 9: Linear measurement. Millimeters,
Meters and kms Using meter-scale, measuring tapes, etc.. We measure Length in 9 More details
Slide 10: PERIMETER He runs 2 equal lengths (2l units)and
2 equal breadths(2b units) Consider a boy running around a rectangular field. Length ( l ) Breadth (b) 10 Length ( l ) Breadth (b) How much distance did he run? Thus he runs 2l + 2b = 2(l+b)units
This is called as perimeter of the rectangle Slide 11: PERIMETER He runs 4 equal lengths s+s+s+s units)and
Thus he runs s+s+s+s = 4s units
This is called as perimeter of a square. Consider a boy running around a Square field.
How much distance did he run? Side (s) 11 Side ( s) Side (s) Side (s) Slide 12: PERIMETER The perimeter (or ) circumference is the distance covered by the boy.
The Circumference of a circle = 2r units
Where = 3.14 = 22/7 Consider a boy running around a circular field 12 Radius = r ? Click here Slide 13: 13 Find the perimeter of the colored plane figures Slide 14: Surface measurement Area is the surface occupied by a plane figure. Area is the product of two linear measurement of same unit.
It occupies several squares. We measure Surface as Areas. Ex:
The mat spread on the floor occupies some space.
The cost of painting the wall depends on the Space which is to be painted 14 Slide 15: Basic formula for areas Area of a square= s x s Square units Area of a Rectangle= l x b Square units 15 Slide 16: Parallelogram Area of a parallelogram = b x h Square units b = Base Length h = height 16 Slide 17: h=height b = base Area of Right handed Triangle = ½ b x h Square units ½ bxh ½ bxh Area of Right handed Triangle 17 Slide 18: Find the area of the following plane figures if each square has side 1 cm. 18 Slide 19: Find the area of the following plane figures if each square has side 1 cm. 19 Slide 20: 20 Find the area of the colored plane figures Slide 21: 21 Circle Area formula:
Area of a circle = x r x r = r 2 sq. units ? Click here Diameter (d)
‘r’ Major segment Minor segment Chord Sector Slide 22: 22 What is ? (sometimes written pi) is a mathematical constant whose value is the ratio of any circle‘s circumference to its diameter in Euclidean space ; this is the same value as the ratio of a circle's area to the square of its radius. It is approximately equal to 3.141593 in the usual decimal notation.
(Ref: Wikipedia) Back Slide 23: 23 RECAP Slide 24: 24 ACTIVITY-1 Observe the following models given to you. Equilateral triangle Side = s units Side = s units ½ s units ½ s units Slide 25: Side = s units Side = s units Side = s units 25 ACTIVITY-2 Observe the following models given to you. Hexagon Side = s units Side = s units Slide 26: 26 ACTIVITY - 3 Derive a formula to find the perimeter of an equilateral triangle.
Derive the formula to find the height of an equilateral triangle (Use Pythogorous theorem)
Derive a formula to find the area of an equilateral triangle.
Derive a formula to find the perimeter of a regular hexagon.
Derive a formula to find the area of a regular hexagon. Derive the following formula using the models given to you. Pythogorous theorem Slide 27: 27 PYTHOGOROUS THEOREM Theorem:
In a Right angled triangle
Square of the hypotenuse = sum of the squares of other two sides BACK NEXT LESSON [ Hypotenuse is the
side opposite to 90o ] By theorem AC2 = AB2 + BC2
i.e., z2 = x2 + y2.
x2 = z2 y2. Slide 28: 28 Volume Volume is the space occupied by an object
(Space is 3 dimensional)
Ex: Juice in a container.
Milk in a vessel.
Volume is the product of three measurements of same unit. [ Length x Breadth x Height for a rectangular vessel ] More details Slide 29: 29 Volume Basics-1 10cm 5 cm 12 x 1 = 12 cm Volume = Base area x Height = A x h = (l x b) x h Cubic units Slide 30: 30 Volume Basics-2 Volume = Base area x Height = ( r2 ) x h = r2 h Cubic units Here the area of the base = Area of the circle = r2 sq. units Slide 31: Volume of a cuboid Length = 4 units Breadth = 3 units Height = 3 units Volume of a Cuboid = Length x Breadth x Height = l x b x h = lbh cubic units. Slide 32: Volume of a cube side = 3 units Side = 3 units Side = 3 units Volume of a Cube = Side x Side x Side = SxSxS= S3 cubic units. Slide 33: 33 EVALUATION-1 The Perimeter of a square is _______
Area of a square is ________
The perimeter of a rectangle is __________
Area of a Rectangle is _________
The circumference of a circle is _________
The area of a circle is __________
The area of a right angled triangle is ____________
The area of a parallelogram is __________
The perimeter of an equilateral triangle is _______
The height of an equilateral triangle _________
The area of an equilateral triangle __________
The perimeter of a regular hexagon___________
The area of a regular hexagon _____________ l x b sq. units. s2 sq. units. 4s units. 2 ( l + b ) units. 2r units. r 2 sq. units. ½ (bxh) sq. units. bxh sq. units. 3s units. 6 s units. Slide 34: EVALUATION-2 The volume of a right angular solid is ________________
The volume of a cube is ________
The volume of a cuboid is __________
The volume of a cylinder is _________ (r 2 ) h cu. units. s3 cu. units. (Base area x Height )cu.Unit ( l x bxh ) cu. units. Slide 35: Find the area of the colored plane region 9 sq. cm 2 sq. cm 2 sq. cm 1 sq.cm 10 sq. cm 6 sq. cm 2 sq. cm 1 sq.cm 1 sq.cm 35 EVALUATION-3 Slide 36: Find the area of the graveled path 36 EVALUATION-4 Slide 37: Find the volume of the following shapes: 37 EVALUATION-5 Slide 38: Find the volume of the following shapes: 38 EVALUATION-6 Slide 39: Find the volume of the following shape: 39 EVALUATION-7 Slide 40: END OF THE