Lessons

1. Basics
 2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
5 - Quadrilaterals
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

 

Areas of Polygons

Objective:

             • Learning and using the formulas for the areas of rectangles, parallelograms, triangles, rhombuses, trapezoids, and regular polygons

           • Learning the basics of the area of a polygon

       

Lesson 11-1 Areas of Polygons:

             Base: Any side of a rectangle or other parallelogram

           Altitude: Any segment perpendicular to the line containing the base from any point on the opposite side

            Height: The length of an altitude.

                Center of a regular polygon: The center of the circumscribed circle

              Radius of a regular polygon: The distance from the center to a vertex

              Central angle of a regular polygon: An angle formed by two radii drawn to consecutive vertices

              Apothem of a regular polygon: The Perpendicular distance from the center of the polygon to a side

 

Postulate 17

The area of a square is the square of the length of a side. (A=s2)

 A=s2 = 22 = 4  Area of the square if 4

 

Postulate 18

If two figures are congruent, then they have the same area.

 

Postulate 19

The area of a region is the sum of the areas of its non-overlapping parts.

 Area of ABCD = Area I +Area II

 

Theorem 11-1

The area of a rectangle equals the product of its base and height. (A = bh)

 Area of ABCD = bh = 10(2) = 20

 

Theorem 11-2

The area of a parallelogram equals the product of a base and the height to that base (A=bh)

 Area of ABCD = bh = 20(10) = 200

 

Theorem 11-3

The area of a triangle equals half the product of a base and the height to that base. (A=1/2 bh)

 Area of Triangle ABC = 1/2 bh = 1/2(5)(10) = 25

 

Theorem 11-4

The area of a rhombus equals half the product of its diagonals (A= 1/2D1D2)

AC= D1= 10       DB= D2= 5

Area of Rhombus = 1/2 D1D2 = 1/2 (10) (5)= 25

 

Theorem 11-5

The area of a trapezoid equals half the product of the height and the sum of the bases. (A = 1/2 h (b1 + b2))

 Area of ABCD = 1/2 h (b1 + b2) =1/2 (3) (8+10)=27

 

Theorem 11-6

The area of a regular polygon is equal to half the product of the apothem and the perimeter. (A= 1/2ap)

 Area of Polygon = 1/2 ap =1/2 (8) (5)=20

 

 

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