## Perimeter and Area

Multiplication Tables: the product of two numbers can be represented by the area of a rectangle where the factors are represented as the dimensions of the rectangle. Notice each square in the area grid is a unit square.

Area of a rectangle is represented by a grid of unit squares. Perimeter is the distance around the outside rectangle.

Area of a square is represented by a grid of unit squares. Perimeter is the distance around the outside square.

Area of a parallelogram is represented by a grid of unit squares. Perimeter is the distance around outside of the parallelogram.

Area of a rhombus is represented by a grid of unit squares. Perimeter is the distance around outside of the rhombus.

Area of Triangles is represented by a grid of unit squares. Perimeter is the distance around outside of the triangle.

Area of Trapezoids is represented by a grid of unit squares. Perimeter is the distance around outside of the trapezoid.

Shape Explorer - perimeter and area on a grid

Maximize Area

Minimize Perimeter

Interactive sums

 Polygon/Circle P = Perimeter C = Circumference distance around the polygon/circle A = Area the surface inside the boundary( perimeter) triangle a = altitude b = base P = b + c + d or P = s1 + s2 + s3 A = 1/2ab Note: The area of the triangle is half the area of the corresponding parallelogram/rectangle. quadrilateral P = b + c + d + e or P = s1 + s2 + s3 + s4 don't need to memorize the formula in junior high enrichment trapezoid a = altitude b = base P = b1 + b2 + c + d or P = s1 + s2 + s3 + s4 A = 1/2ab1 + 1/2ab2) simplifies to A = 1/2a(b1 + b2) parallelogram a = altitude b = base P = 2b + 2c A = bh rhombus a = altitude s = side length P = 4s A = as rectangle l = length w = width P = 2l + 2w A = lw square s = side length P = 4s A = s2 chevron P = 2c + 2d don't need to memorize the area formulae in junior high kite P = 2c + 2d don't need to memorize the area formulae in junior high enrichment regular polygon a = apothem length s = side length n = #sides   pentagon = "five sides" hexatagon = "six sides" heptaagon = "seven sides" octaagon = "eight sides" nonagon = "nine sides" decagon = "ten sides" P = ns A = 0.5ans = 0.5aP circle Circumference is the distance around the circle. r = radius of circle d = diameter of circle C = Circumference C = pd A = Area A = p r2 Relationships: 1. For a square, non-square rectangle and circle with equal perimeter/circumference the relative area from largest to smallest is: 2. Increasing dimensions by a factor increases the perimeter by the same factor. tripling the dimensions triples the perimeter 1. For a square, non-square rectangle and circle with equal areas the relative perimeter from largest to smallest is: 2. Increasing the dimensions by a factor increases the area by the square of the factor. tripling the dimensions increases the area by a factor of 9 (32). Polygon/Circle Perimeter/Circumference

Study the surface area and volume for the prisms, pyramids, cylinder and cone provided.