Area of Plane Figures

1
Area of Plane Figures

• Area formulas
• Parallelogram A bh
• Triangle A ½ bh
• Rhombus A ½ d1 d2
• Trapezoid A ½ (b1 b2 ) h
• Rectangle A bh or A lw
• Square A s2 or
• rhombus or
• rectangle or
• parallelogram
• Circle A P r2
• C 2 P r
• Area of Sector A x (P r2)
• 360
• Length of Sector L x (2P r)
• 360
• And combinations of the above

2
Areas of Rectangles

• Rectangle A bh or A lw
• Square A s2
• 1)
• 3) Area of a square 48 find a side.
• 4) The diagonal of a rectangle is 25 if one side
  is 7 find the area of the rectangle.
• Area of a region equals the sum of the areas of
  non-overlapping parts

2)
4
2
4
5
4
3
1
1
3
Areas of Parallelograms, Triangles, and Rhombi

• Parallelogram A bh
• Triangle A ½ bh
• Rhombus A ½ d1 d2
• Be sure to use the perpendicular height!
• Remember special relationships (isos. Triangles
  and altitudes 30-60-90 etc)
• Examples, find the areas

4
Areas of parallelograms, etc

• More examples--find the area
• 5) Rhombus 6)
• 7) Find the area of an isosceles triangle with
  base 16 and side 12.
• 8) Find the area of a parallelogram with a 45
  degree angle and sides 4 and 15

8
5
11-3 Area of a trapezoid

• Trapezoid A ½ (b1 b2 ) h
• or A m h where
  mmedian
• (A trapezoid can be viewed as two triangles and a
  rectanglesometimes this is necessary other times
  this is more time consumingremember time
  points on the ACT.)
• Examples
• 1) 2)
• 3) 4)

6
Review

• Review all formulas and types of problems using
  the text book and going over the quiz and the
  review sheets.
• Polygons (This is review and needed for tomorrow)
• Sum of the interior angles of any convex polygon
  is
• (n-2) ( 180) sum of interior lts
• Sum of the exterior angles of any convex polygon
  360
• Regular Polygon? all sides and all angles
• Regular Polygons have all angles and sides
  congruent.
• Since all angles are then we can find just one
  angle by dividing the sums by sides
• Sum of the interior lts 1 interior lt
• Sides
• 1 exterior lt 360 and n
  360
• n ext. lt

7
11-4 Area of regular figures

• Regular convex polygon
• all sides are
• all angles are
• Area of a regular convex polygon
• A ½ a p
• Special segments in the polygon
• r radius -bisects the angle from center to
  vertex
• a apothem -drawn from center to midpoint of
  side is __
• p-perimeter of the polygon

8
11-4 Regular Figures (cont)

• Find the area of the given figures
• 1) Find the area of a regular hexagon with
  apothem 9
• 2) Find the an equilateral triangle with side 12.
• 3) Find the area of a square with radius 4Ö2
• 4) Find the area of a regular hexagon with
  perimeter 48.
• 5) Find the area of a regular pentagon with
  apothem 3.

9
11-5 Circumference and Area of Circles

• Circle A P r2
• C 2 P r
• Pi P is the ratio of circumference to diameter
• It is constant for all circles and can be
  approximated as 3.14 or 22/7
• Use 22/7 for use with fractions-especially with
  multiples of 7.
• Always leave answers in P form unless told to
  approximate.
• Examples
• 1) Find C and A if r 15.
• 2) Find r, d, and A if C 26 P
• 3) Find r, d, and C if A 18 P
• 4) If a bicycle tire has a diameter of 26 in.,
  how fat does it travel in 1000 revolutions?
• Word problemsdraw and label
• be careful these can sound tricky!

10
11-6 Sectors of circles

• Sector of a circle is part of a circle -- similar
  to a pie wedge--its size is related to
• the central angle formed by the radii
• and by the length of the radius
• Formulas
• Area of Sector A x (P r2)
• 360
• Length of Sector L x (2P r)
• 360
• Examples
• 1) 2)
• 4) 5)

11
11-8 Ratios of areas and similar figures

• Similar figurescongruent angles and proportional
  sides (Chapter 7)
• Scale factorproportionality constant
• Scale factor of sides a/b
• Ratio of perimeter a/b
• Ratio of areas a2 / b2
• Example
• 1) scale factor 2/7
• Find the ratios of perimeter and area
• 2) ratio of area 36/121
• Find the ratio of perimeter and the scale facto