18.01 Area & Perimeter of Rectangles

A rectangle is a quadrilateral with four right angles Height (h) Base (b) Every rectangle has a base (b) and a height (h). Perimeter is the distance around the figure. Area is the number of squares needed to cover the inside of a figure.

Perimeter Formula of a Rectangle: Height (h) P = 2b + 2h Base (b) Area Formula of a Rectangle: A = b • h Find the perimeter and area of a rectangle whose base = 4 in. and whose height = 3 in. P = 2b + 2h = 2(4 in.) + 2(3 in.) = 8 in. + 6 in. = 14 in. A = b • h = 3 in. • 4 in. = 12 in2

A square is a rectangle with 4 equal sides (b) Since the b = h = s, the formulas can be changed. Perimeter Formula of a Square: P = 4 • s Area Formula of a Square: A = s2 Find the perimeter and area of a square whose side = 9 cm. P = 4 • s = 4 • 9 cm = 36 cm A = s2 = (9 cm)2 = 81 cm2

Height (h) Base (b) To find a missing side given its area, replace the variables in the formula with their numbers and solve. Find the missing side. b = 6 m and A = 54 m2 A = b • h 54 m2 = 6 m • h 9 m = h

To find the area or perimeter of a rectangle given one side and a diagonal, use the Pythagorean Theorem to find missing side. a2 + b2 = c2 (x)2 + (4)2 = (5)2 5 m x m x2 + 16 = 25 x2 = 9 4 m x = 3 P = 2b + 2h = 2( 4 m) + 2(3 m) = 8 m + 6 m = 14 m A = b • h = 4 m • 3 m = 12 m2