Perimeter of Regular and Irregular Shapes
Perimeter in Grade 4 is formalized: it is the sum of all side lengths. For regular polygons, this simplifies to n x side length. For irregular polygons, every side must be measured and added. The geoboard is the ideal tool because it allows students to build shapes, adjust them, and measure simultaneously. Perimeter has immediate practical applications: fencing a garden, framing a picture, bordering a floor.
Perimeter as the sum of all sides
For any polygon: perimeter = sum of all side lengths. Regular hexagon with side 4 cm: P = 6x4 = 24 cm. Irregular quadrilateral with sides 3, 5, 4, 7 cm: P = 3+5+4+7 = 19 cm. The formula for regular polygons (n x side) is a shortcut for repeated addition of equal sides.
Finding missing side lengths
A pentagon has perimeter 30 cm. Four sides are 7, 6, 5, and 8 cm. What is the fifth? 7+6+5+8=26. 30-26=4 cm. This reversal requires understanding that perimeter is the sum: if we know the total and all but one part, subtraction gives the missing part. This is an equation: 26+n=30.
Real-world perimeter applications
Fencing: a rectangular garden 12 m x 8 m needs fencing on all 4 sides. Perimeter = 2x(12+8) = 2x20 = 40 m of fencing needed. Picture frame: a 20 cm x 15 cm photo needs a frame. Perimeter = 2x(20+15) = 2x35 = 70 cm of framing material. These contexts give perimeter immediate practical value.