MAT 150 Unit 20

1
MAT 150 Unit 20

• Ch 18 2 and 18 3
• Area and Perimeter

2
Section 18 2 Triangles and Quadrilaterals

• Triangle three sides a, b, c, with height h
• a h c
• b
• Perimeter
• P a b c
• Area
• A ½ bh

3
Section 18 2 Triangles and Quadrilaterals

• Quadrilaterals
• Square all sides have the same measure, s, with
  four 90o angles
• s
• s
• Perimeter
• P 4s
• Area
• A s2

4
Section 18 2 Triangles and Quadrilaterals

• Quadrilaterals
• Rectangle opposite sides are of equal measure
  and parallel and four 90o angles
• w
• l
• Perimeter
• P 2(l w)
• Area
• A lw

5
Section 18 2 Triangles and Quadrilaterals

• Quadrilaterals
• Parallelogram opposite sides are of equal
  measure and parallel
• s h
• b
• Perimeter
• P 2(b s)
• Area
• A bh

6
Section 18 2 Triangles and Quadrilaterals

• Quadrilaterals
• Trapezoid one pair of sides are parallel
• b1
• a h c
• b2
• Perimeter
• P a b1 b2 c
• Area
• A ½ h(b1 b2 )

7
Section 18 2 Triangles and Quadrilaterals

• A carpet installer is carpeting a 16 ft. X 20 ft.
  room. Projecting out into the room is a
  fireplace hearth measuring 3 ft. X 6 ft. How
  many square yards of carpet is needed for the
  job? How much is wasted?
• 
  
• 
  3
• 
  6
• 16
• 20

8
Section 18 2 Triangles and Quadrilaterals

• A carpet installer is carpeting a 16 ft. X 20 ft.
  room. Projecting out into the room is a
  fireplace hearth measuring 3 ft. X 6 ft. How
  many square yards of carpet is needed for the
  job? How much is wasted?
• Area of room A lw
• A (16 ft.)(20
  ft.) 320 sq. ft or 320 ft.2
• Area of hearth A lw
• A (3 ft.)(6 ft.)
  18 sq. ft. or 18 ft.2
• So youll need 320 sq. ft. of carpet. Since 1
  sq. yd. 9 sq. ft. it would be 320
  sq. ft. X 1 sq. yd. 320 35 5/9 or 36 sq.
  yds.
  
  1 9 sq. ft.
  9
• Wasted would be 18 sq. ft. X 1 sq. yd 2 sq.
  yds.
• 1
  9 sq. ft.

9
Section 18 2 Triangles and Quadrilaterals

• Herons Formula
• In a triangle where all the sides are known but
  not the height use Herons formula to calculate
  the area.
• A s (s a)(s b)(s c)
• Where s ½ (a b c)
• a b
• c

10
Section 18 2 Triangles and Quadrilaterals

• Find the missing dimensions x and y
• y
• x
• 18 m
• 14 m
  30 m
• 40 m
• Think of the complete figure as one big
  rectangle, (dotted line area added)
• Since opposite sides of each rectangle are equal
  then
• 18m y 40m and 14m x 30m
• y 22m and x 16m

11
Section 18 2 Triangles and Quadrilaterals

• To find the area of the figure you could
• 22 m
• 16 m
• 18 m
• 14 m
  30 m
• 40 m
• Find the area of the large rectangle including
  the dotted line area (40 m X 30 m 1200 m2)
• Find the area of the dotted line rectangle (18m X
  16 m 288m2)
• Then subtract 1200 m2 288m2 912m2
• 
  OR

12
Section 18 2 Triangles and Quadrilaterals

• 22 m
• 16 m
• 18 m
• 14 m
  30 m
• 40 m
• Find the area of the blue rectangle area (22 m X
  30 m 660 m2)
• Find the area of the red rectangle (18m X 14 m
  252m2)
• Then add 660 m2 252m2 912m2
• 
  

13
Section 18 3 Circles and Composites

• Circle
• d
• 
  
• r
  
• Perimeter is called Circumference
• C d or 2 r
• Area
• A r2

14
Section 18 3 Circles and Composites

• Find the circumference and area for a circle with
  a diameter of 1.3 m.
• Circumference
• C d (3.14)(1.3m) 4.082 m
• Area
• A r2 since r ½ d, r 0.65m
• A (3.14)(0.65m)2 (3.14)(.4225 sq m) 1.33
  sq. m

15
Section 18 3 Circles and Composites

• Composite figures- are two or more figures that
  make up the overall figure.
• Example Find the area of a washer15 in in
  diameter with a 3 inch diameter opening.

15
3
16
Section 18 3 Circles and Composites

• Find the area of a washer15 in in diameter with a
  3 inch diameter opening.
• To find the area of the composite figure you
  would need to find the area of the large circle
  and subtract from it the area of the small.

17
Section 18 3 Circles and Composites

• Large circle
• A r2
• A (3.14)(7.5)2 176.625 sq. in.
• Small circle
• A r2
• A (3.14)(1.5)2 7.065 sq. in.
• So the area of the washer is
• 176.625 7.065 169.56 sq. in.