Equivalency in Plane Figures - RULES - 4.05 Equivalency in Plane Figures - RULES -

Equivalent Plane Figures If 2-dimensions shapes have the same area, they are said to be EQUIVALENT.

Definition: “Regular” When a polygon is referred to as “regular” it means that all of the sides are the same length

Comparing Equivalent Quadrilaterals -Find the Area and Perimeter 6 cm 4 cm 9 cm   3cm 12 cm 2 cm 18 cm What do you notice?

Comparing Equivalent Triangles -Find the Area and Perimeter B=2 cm H=18 cm B=9.5244 cm H=8.2484 cm B=4 cm H=9 cm What do you notice?

Rule # 1 Of all equivalent polygons with the same number of sides, the regular polygon will always have the smallest perimeter

“Flip” Rule #1 Of all polygons with the same number of sides and the same perimeter, the regular polygon will have the greatest area

TEST Rule # 1 Flipped 6 cm   2cm 10 cm

Comparing Equivalent Polygons -Find Area and Perimeter 25 cm 25.12 cm 28.06 cm 17.72 cm 21.94 cm 13.51 cm 9.29 cm 11 cm 9.53 cm 10 cm

Rule #2 Of all equivalent polygons, the one with the greatest number of sides will always have the smallest perimeter

Flip Rule #2 Of all polygons with the same perimeter, the one with the most sides will have the greatest area

TEST Rule # 2 Flipped 6 cm 12 cm 12 cm 12 cm 5.196152 cm 12 cm 6cm   6cm 12 cm 6 cm 12 cm 12 cm 5.196152 cm 12 cm 5.729577951 cm