Math 103-Mensuration-Areas-sem-dfs
•Télécharger en tant que PPTX, PDF•
0 j'aime•3,488 vues
Mathematics for Interior Design- Geometry-Plane Mensuration-Area- by Dr. Farhana Shaheen-KSA
Recommandé
Contenu connexe
Tendances
Tendances (20)
En vedette
En vedette (20)
Similaire à Math 103-Mensuration-Areas-sem-dfs
Similaire à Math 103-Mensuration-Areas-sem-dfs (20)
Plus de Farhana Shaheen
Plus de Farhana Shaheen (20)
Dernier
Dernier (20)
Math 103-Mensuration-Areas-sem-dfs
- 1. MENSURATION MATH-103 Mathematics for Interior Design Dr. Farhana Shaheen
- 2. MENSURATION Mensuration is to measure the quantities such as perimeter, area, volume, length of a closed geometrical figure. If we want to build a house or planning a garden, we need to know exactly the space we have and the amount of space we need. For the purpose for these we have to calculate the length of the boundary and space occupied. In other words we have to determine the perimeter and area of the plot. 2 Free powerpoint template: www.brainybetty.com
- 4. DEFINITION: MENSURATION Mensuration is a branch of Mathematics which deals with the measurements of lengths of lines, areas of surfaces and volumes of solids. Mensuration may be divided into two parts: 1. Plane Mensuration (for 2 dimension) 2. Solid Mensuration (for 3 dimension) 4 Free powerpoint template: www.brainybetty.com
- 5. SHAPES IN 2-D AND 3-D
- 6. PLANE MENSURATION Plane Mensuration deals with perimeter, length of sides and areas of two dimensional figures and shapes. For example, Circle, Semi-circle Rectangle Pentagon Semi-circle Triangles, Trapezium, etc. 6 Free powerpoint template: www.brainybetty.com
- 7. SOLID MENSURATION Solid mensuration deals with areas and volumes of solid objects in three dimensions. For example: Polyhedrons, Cylinders, Cones, Spheres. They are called Space Figures. 7 Free powerpoint template: www.brainybetty.com
- 8. SPACE FIGURES Polyhedrons are space figures with flat surfaces, called faces, which are made of polygons. Prisms and pyramids are examples of polyhedrons. A cylinder has two parallel, congruent bases that are circles. A cone has one circular base and a vertex that is not on the base. A sphere is a space figure having all its points an equal distance from the center point. Note that cylinders, cones, and spheres are not polyhedrons, because they have curved, not flat, surfaces.
- 10. Here is an interesting and lovely way to look at the beauty of mathematics, and of God, the sum of all wonders. The Beauty of Mathematics Shapes of Numbers Wonderful World 10 Free powerpoint template: www.brainybetty.com
- 11. 11 Trapezium Definition: A trapezium is a shape with four sides, that has one set of parallel sides. Free powerpoint template: www.brainybetty.com
- 12. 1 x 8 + 1 = 9 12 x 8 + 2 = 98 123 x 8 + 3 = 987 1234 x 8 + 4 = 9876 12345 x 8 + 5 = 98765 123456 x 8 + 6 = 987654 1234567 x 8 + 7 = 9876543 12345678 x 8 + 8 = 98765432 123456789 x 8 + 9 = 98765432112 Free powerpoint template: www.brainybetty.com
- 13. 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 123456 x 9 + 7 = 1111111 1234567 x 9 + 8 = 11111111 12345678 x 9 + 9 = 111111111 123456789 x 9 +10= 1111111111 13 Free powerpoint template: www.brainybetty.com
- 14. 9 x 9 + 7 = 88 98 x 9 + 6 = 888 987 x 9 + 5 = 8888 9876 x 9 + 4 = 88888 98765 x 9 + 3 = 888888 987654 x 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888 Brilliant, isn’t it? 14 Free powerpoint template: www.brainybetty.com
- 15. 0 x 9 + 8 = 8 9 x 9 + 7 = 88 98 x 9 + 6 = 888 987 x 9 + 5 = 8888 9876 x 9 + 4 = 88888 98765 x 9 + 3 = 888888 987654 x 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888 987654321 x 9 - 1 = 8888888888 9876543210 x 9 - 2 = 88888888888 15 Free powerpoint template: www.brainybetty.com
- 16. 1 x 1 = 1 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 111111 x 111111 = 12345654321 1111111 x 1111111 = 1234567654321 11111111 x 11111111 = 123456787654321 111111111 x 111111111 = 12345678987654321 And look at this symmetry: 16 Free powerpoint template: www.brainybetty.com
- 17. TAKE A LOOK AT THIS SYMMETRY: RIGHT ANGLED TRIANGLE 1 x 1 = 1 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 111111 x 111111 = 12345654321 1111111 x 1111111 = 1234567654321 11111111 x 11111111 = 123456787654321 111111111 x 111111111 = 12345678987654321 17 Free powerpoint template: www.brainybetty.com
- 19. AREA OF CLOSED FIGURES The measure of region enclosed in a closed figure is called Area. For example, we need to find the areas of Polygons, Circles, or any other closed figures. http://www.helpingwithmath.com/by_subject/geomet ry/geo_area.htm 19 Free powerpoint template: www.brainybetty.com
- 21. CONCEPT OF AREA AND ITS USES IN DAILY LIFE SITUATIONS There are two vacant rooms in a school numbered as 3 and 4. Students of class-VI are to take their mid-day meals. The monitor was asked to make arrangements for the students of his class in room number 3. He said “Students of our class cannot be accommodated in Room No.3, but they can be accommodated in Room No. 4”. What could be the difference between the two rooms so that one of these can accommodated the students of Class VI whereas the other one cannot accommodate it? The general answer will be Room No. 4 is bigger than Room No. 3. It is because the region enclosed within Room No. 4 is greater than Room No. 3. Thus, the measure of region enclosed in a closed figure is called Area. http://www.helpingwithmath.com/by_subject/geometry/g eo_area.htm 21 Free powerpoint template: www.brainybetty.com
- 22. UNIT OF MEASUREMENT OF AREA To measure anything we first fix a unit to be used to measure it such as: To measure a length, you use a meter as a unit. Area is measured in square unit like 3 m or 5 cm . TABLE FOR AREA NAME AREA Rectangle Length*breadth = L W Square Side*Side = s Triangle 1/2 Base*Altitude = ½ b h Parallelogram Base*Altitude = b h Trapezium 1/2*h (Sum of two parallel side) = ½ h (a + b) 2 2 22 2 Free powerpoint template: www.brainybetty.com
- 23. TRIANGLES A triangle has three sides and three angles. The three angles always add to 180° There are three special names given to triangles that tell how many sides (or angles) are equal. There can be 3, 2 or no equal sides/angles: Equilateral Triangle has all 3 sides equal Isosceles Triangle has 2 sides equal Scalene Triangle has No sides equal 23 Free powerpoint template: www.brainybetty.com
- 24. EQUILATERAL, ISOSCELES AND SCALENE Equilateral Triangle Three equal sides Three equal angles, always 60° Isosceles Triangle Two equal sides Two equal angles Scalene Triangle No equal sides No equal angles 24 Free powerpoint template: www.brainybetty.com
- 25. WHAT TYPE OF TRIANGLE? Acute Triangle All angles are less than 90° Right Triangle Has a right angle (90°) Obtuse Triangle Has an angle more than 90° 25 Triangles can also have names that tell you what type of angle is inside: Free powerpoint template: www.brainybetty.com http://home.avvanta.com/~math/triangles.html
- 26. EXAMPLE: TO FIND AREA OF A TRIANGLE To find the area of the Triangle we should know the base and altitude(height) Area of the triangle=1/2*base*altitude Exp:1 Find the area of the triangle which base is 6 m and altitude is 8 m? Solution: Here, Base of the triangle= 6 m Altitude of the triangle = 8 m Area of the Triangle= 1/2*base*altitude = 1/2*6*8 = 24 m2 26 Free powerpoint template: www.brainybetty.com
- 27. Free powerpoint template: www.brainybetty.com 27 AREA OF A TRIANGLE ½ Base x Height = Area (It’s ½ because ½ of the “square” is missing) Base Height Height Base 8 5 ½ Base x Height = Area ½ (8) x 5 = Area 4 x 5 = 20
- 28. 28 AREA OF PARALLELOGRAM Area=Base x Height = bh (Area=length x width) BASE (length) Height (width) 8 5 Base 8 x Height 5 = Area 40 The diagonal line is NOT the height!!! Free powerpoint template: www.brainybetty.com
- 29. TO FIND AREA OF A TRAPEZIUM Trapezium: 29 Free powerpoint template: www.brainybetty.com
- 30. 30 Trapezium Definition: A trapezium is a shape with four sides, that has one set of parallel sides. Trapezium/Trapezoid Formula : Area of Trapezium = ½ (a + b)h where a, b = sides, h = height Free powerpoint template: www.brainybetty.com
- 32. EXAMPLE: TO FIND AREA OF A TRAPEZIUM To find the area of the Trapezium, we should know the altitude(height)and sides Ques: Find the area of the Trapezium which height is 4 m and sides are 10 m and 12 m? Solution: Here, height of the Trapezium=h= 4 m Side of one Trapezium= a = 10 m Side of another Trapezium= b = 12 m Area of the Triangle = 1/2*h(a + b) =1/2*4(10+12) = 44 m2 32 Free powerpoint template: www.brainybetty.com
- 33. Free powerpoint template: www.brainybetty.com 33 DIFFERENT NAMES/SAME IDEA Length x Width = Area Side x Side = Area Base x Height = Area
- 34. QUESTION: FIND THE AREA OF THE GIVEN SCALENE TRIANGLE 34 Free powerpoint template: www.brainybetty.com Example: What is the area of this triangle? Height = h = 12 Base = b = 20 Area = ½ × b × h = ½ × 20 × 12 = 120 Note: The base can be any side, Just be sure the "height" is measured at right angles to the "base“.
- 35. Can you find the Areas of these closed figures? 35 Free powerpoint template: www.brainybetty.com
- 39. EULER DIAGRAM OF QUADRILATERAL TYPES Kite Quadrilateral 39
- 40. NAME THE SEVEN QUADRILATERALS AND FIND THEIR AREAS. 40 Free powerpoint template: www.brainybetty.com
- 41. QUICK CHECK: i. The sum of all angles in a triangle is ___________ degrees. ii. The area of a triangle is __________________________ iii. The area of a trapezium is ______________________ iv. _____________ triangle has two sides equal. 41 Free powerpoint template: www.brainybetty.com
- 42. QUICK CHECK: o v. _______________triangle has one 90 degree angle o vi. _______________ triangle has all angles and sides are the same. vii. ________________ triangle: Has all three angles and all three sides different. viii. The interior angles of a simple quadrilateral ABCD add up to ______ degrees. 42