Slide 1 : Geometry Exploring Area and Perimeter
Slide 2 : What You'll LearnWhy You Should Learn It How to find the perimeter of a polygon How to find the area of a square and rectangle
You can use perimeters and areas to solve real-life problems, such as finding the amount of fertilizer to cover a lawn
Slide 3 : Perimeter The perimeter of a polygon is the sum of the length of its sides
Linear Measurement (cm, m, in, ft, mi, etc.)
Slide 4 : Example 1 Use a compass and straightedge to construct a segment whose length is equal to the perimeter of PQRS
Slide 5 : Example 1 Draw a long segment Use your compass to measure each segment P Q R S P PQ + QR + RS + SP = Perimeter of PQRS
Slide 6 : Areas of Squares & Rectangles Area of a polygon is the number of square units contained in its interior
Areas are measured in square units such as m2 or ft2 3 3 1 2 3 4 5 6 7 8 9 9 units2
Slide 7 : All formulas for areas of polygons based on these 3 postulates Postulate 22 - Area of a Square Postulate: The area of a square is the square of the length of its side, or A = s2
Postulate 23 – Area Congruence Postulate: If two polygons are congruent, then they have the same area
Postulate 24 – Area Addition Postulate: The area of a region is the sum of the areas of all its non-overlapping parts
Slide 8 : Theorem 11.1 Area of a Rectangle Theorem:
The area of a rectangle is the product of its base and height, or A = bh
The base and height meet at right angles h b
Slide 9 : Example 2 Each of the three rectangles has a height of 6 units and a base of 4 units. Each is composed of congruent polygons. Find the area of each polygon
Slide 10 : Example 2 Each of the three rectangles has a height of 6 units and a base of 4 units. Each is composed of congruent polygons. Find the area of each polygon 1 1 Twenty-four 1 unit by 1 unit squares 1 Square Unit Twelve 1 unit by 2 unit squares 1 2 2 Square Units Six congruent hexagons 24÷6 =4 4 Square Units
Slide 11 : Example 3Comparing Perimeters and Areas of Squares Find a pattern for the perimeters and a pattern for the areas of the following squares. Graph your results and find functions that give the perimeter and area in terms of the side lengths
Slide 12 : Example 3 Begin by making a table that shows the perimeter and area of each square
Slide 13 : Begin by making a table that shows the perimeter and area of each square Example 3
Slide 14 :
Slide 15 : P = 4s A = s2
Slide 16 : THE END