Maths for Interior Design-Plane Mensuration-Perimeter- by Dr. Farhana Shaheen

1. PLANE MENSURATION- II
PERIMETER
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.
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3. 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)
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4. SHAPES IN 2-D
AND 3-D

5. 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.
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6. PLANE MENSURATION
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7. PERIMETER
 The measure of region enclosed in a closed figure
(inside the figure) is called Area.
 A Perimeter is a path that surrounds an area. The
word comes from the Greek peri (around) and
meter (measure).
 The term may be used either for the path or its
length - it can be thought of as the length of the
outline of a shape.
 Calculating the perimeter has considerable practical
applications. The perimeter can be used to
calculate the length of fence required to surround a
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yard or garden.

8. PERIMETER OF CLOSED FIGURES
 For example, we need to find the perimeter of
Polygons, Circles, or any other closed figures.
 http://www.helpingwithmath.com/by_subject/geomet
ry/geo_area.htm
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9. TANGRAMS
 The tangram (Chinese: "seven boards of skill") is a
dissection puzzle consisting of seven flat shapes, called
tans, which are put together to form shapes. The
objective of the puzzle is to form a specific shape
(given only an outline or silhouette) using all seven
pieces, which may not overlap. It was originally
invented in China.
 It is one of the most popular dissection puzzles in the
world.
 A dissection puzzle, also called a transformation
puzzle or Richter Puzzle, is a tiling puzzle where a set
of pieces can be assembled in different ways to produce
two or more distinct
geometric shapes. 9

10. TANGRAMS
10

11. PERIMETER OF A RECTANGLE:
 The perimeter is the distance around all of a
shape.
 Perimeter of a rectangle:
P = w + l + w + l = 2 (l + w)
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12. Trapezium:
A trapezium is a shape with four sides, that
has one set of parallel sides.
What is the perimeter of a trapezium?
http://www.calculatoredge.com/enggcalc/perim 12
eter.htm#rhombus

13. Trapezium/Trapezoid Formula :
Area of Trapezium = ½×(a + b)×h
where
a, b = sides, h = height
Perimeter of Trapezium = a + b + c + d
where
a, b, c, d = sides of the trapezium.
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14. EXAMPLE: TO FIND PERIMETER
OF A TRAPEZIUM
 To find the perimeter of the Trapezium, we should
know the lengths of all sides.
 Ques: Find the perimeter of the Trapezium with
sides 4 cm, 10 cm,15 cm and 7cm ?
 Solution:
14

15. 1x8+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 = 987654321 15

16. 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 16

17. PERIMETER
 The perimeter of a particular shape is the total length of its sides.
 For a triangle: (p = a + b + c)
 The perimeter is equal to the length of side a, plus the length of
side b, plus the length of side c.
 For a square: (p = 4s)
 The perimeter is equal to 4 times the length of a side.
 For a rectangle: (p = 2 (l + w)
 The perimeter is equal to 2 times the sum of the base plus the
height.
 For regular polygons: ( p = n l)
 The perimeter is equal to the number of sides (n) times the length
(l) of a side.
 Note: Circles do not have sides made of line segments like
polygons do but they do have a perimeter known as a
circumference.
The circumference is equal to 2 times pi times the radius (r). 17

18. PERIMETER
3/13/2013
 Any shape’s “perimeter” is the outside of the
shape…like a fence around a yard.
 To calculate the perimeter of any shape, just add up
“each” line segment of the “fence”.
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19. PERIMETER
The distance around the outside of a rectangle.

20. PERIMETER
3/13/2013
 The distance around the outside of a shape.
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21. SQUARE/RECTANGLE FORMULA
3/13/2013
 Perimeter=2(Length+Width)
 P= 2(25+14) P=2(20+20)
 P= 50+28 P=40+40
 P= 78 P=80
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20
25 21

22. OTHER SHAPES
3/13/2013
 Just add up EACH segment
10
8 sides, each side 10 so 10+10+10+10+10+10+10+10=80
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23. PERIMETER OF A TRIANGLE
Measure each side of the triangle then add
them together.

24. PERIMETER
To find the perimeter you need to measure the
length of each side of the rectangle.
then add them together.

25. PERIMETER
The distance around the outside of a rectangle.
length
width width
length
Perimeter = (2 x L) + (2 x W)

26. RIYAD BANK-YANBU AL SINAIYAH
 How many shapes do you see in this picture?
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27. PYTHAGOREAN THEOREM:
 Pythagorean theorem, a2 + b2 = c2, so A + B = C.
 Generalization for similar triangles Generalization for
green area A + B = blue area C regular pentagons 27

28. UNIT OF MEASUREMENT OF PERIMETER
 To measure anything we first fix a unit to be used to
measure it such as:
 To measure a length, you use a meter, feet, inch,
centimeter as a unit (m, ft, inch, cm).
TABLE FOR PERIMETER
NAME PERIMETER
 Rectangle 2(Length+Width) = 2(l+w)
 Square/Rhombus 4 *Side =4s
 Triangle (a+b+c) Sum of all sides where a, b, and c are
the lengths of the sides of the triangle.
 Parallelogram p = 2(b + h) 28
 Trapezium Sum of all sides

29. 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
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30. TYPES OF TRIANGLES
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31. TYPES OF TRIANGLES
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32. 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 32
No equal angles

33. WHAT TYPE OF TRIANGLES?
Triangles can also have names that
tell you what type of angle is inside:
Acute Triangle
All angles are less
than 90°
Right Triangle
Has a right angle (90°)
Obtuse Triangle
Has an angle more than 90°
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http://home.avvanta.com/~math/triangles.html

34. SSSSSSSSSSSSSSSSS
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35. EULER DIAGRAM OF QUADRILATERAL TYPES
Kite Quadrilateral
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36. NAME THE SEVEN QUADRILATERALS AND FIND
THEIR PERIMETERS
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37. AREA WORD PROBLEMS

38. EXAMPLE 1: FIND THE AREA AND PERIMETER OF
THE GIVEN SCALENE TRIANGLE
Example: What is the area of this triangle?
Height = h = 12
Base = b = 20
Area = ½ b h = ½ 20 12 = 120
To find Perimeter=?
Note: The base can be any side, Just be
sure the "height" is measured at right
angles to the "base“. 38

39. QUESTION 1:
 Find the area of the given trapezium.
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40. QUESTION 2:
 Find the area of the shaded regions, if
 Length of one side of square is s = 4 cm.
 Note:
 Point A is half of s.
 Point D is mid-point
of the square.
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41. QUESTION 3:
 Find area and perimeter of the shaded region.
41

42. PERIMETER WORD
PROBLEMS

43. 1. A REGULAR PENTAGON HAS ONE SIDE 25CM
LONG.
HOW LONG IS THE PERIMETER OF THIS SHAPE?

44. 2. A REGULAR HEXAGON HAS A PERIMETER OF
300CM.
HOW LONG IS THE LENGTH OF ONE SIDE?

45. 3. A SQUARE FIELD HAS A PERIMETER OF
1200M.
HOW LONG IS THE LENGTH OF EACH SIDE OF
THE FIELD?
ONE SIDE OF THE FIELD IS HEDGED. WHAT
LENGTH OF FENCING IS NEEDED TO FENCE IN
THE OTHER THREE SIDES?

46. 4. WHAT IS THE PERIMETER OF A SQUARE
OF SIDE 20CM?

47. 5. IF THE PERIMETER OF SQUARE IS
200CM, THEN WHAT IS THE LENGTH OF ONE
OF THE SIDES?

48. 6. WHAT IS THE PERIMETER OF AN
EQUILATERAL TRIANGLE OF SIDE
8.9CM?

49. 7. A REGULAR HEPTAGON HAS A SIDE
LENGTH OF 26CM. WHAT IS ITS
PERIMETER?

50. 8. A RECTANGLE HAS A PERIMETER OF
68CM.
ITS SHORT SIDE IS 10CM. WHAT IS THE
LENGTH OF THE LONG SIDE?

51.  Can you find the perimeters of these closed
figures?
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52. QUICK CHECK:
 i. The sum of all angles in a polygon is
___________ .

 ii. The area of a triangle is
__________________________

 iii. The perimeter of a trapezium is
______________________

 iv. _____________ triangle has two sides equal.
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53. QUICK CHECK:
o v. _______________triangle has one 90 degree
angle
o vi. _______________ triangle has all angles and
sides same.
 vii. ________________ triangle: Has all three
angles and all three sides different.
 viii. The perimeter of a regular polygon with n
sides is ______ . 53