Perimeter & Area

Section 6.1

Perimeter

• The distance around the outside edges of any flat shape is called the perimeter of the object.

• Think of perimeter as a one dimensional quantity.

• The units of perimeter is length.

• Examples are inches, feet, meters, miles, centimeters, yards, etc.

Area

• Area is the amount of surface inside a flat shape.

• Think of area as a two dimensional quantity.

• The units of area are square length.

• Examples are sq. ft., sq. in., sq. mi. sq m.

• OR ft2, in2, mi2

The square

• Recall that a square is a quadrilateral (an object that has 4 sides). These sides have the same length and the angles made are right angles (an angle that is 90°).

• Let the length of each side be s.

• The perimeter of a square is P = 4s.

• The area of a square is A = s2. s

The Rectangle

• The rectangle is a quadrilateral that has a pair of parallel lines of different lengths. The angles formed by the sides are right angles.

• Let the long side of the rectangle be called the length (L), the other side is the width (W).

• The perimeter is P = 2L + 2W.

• The area is A = LW. L

W

The parallelogram

• The parallelogram is a 4 sided object that has 2 pair of parallel lines. The angles formed by the lines are not right angles.

• To find the perimeter of the parallelogram just sum the sides.

• The area of the parallelogram is A = bh. Think of this object has two triangles put together.

b

h

The trapezoid

• The trapezoid is also a quadrilateral. This object has only on pair of parallel lines.

• The area of the trapezoid is the average of the two bases times the height.

• A = ½ (b1+b2)h b1

h

b2

The circle

• The circle, the most perfect geometric shape. There is no beginning there is no end. Completely symmetric. The circle is the set of all points equidistant from a fixed point called the center. A line segment connecting opposite ends of the circle that goes thru the center is called a diameter (d). The line segment that begins at the center and terminates on the edge of the circle is called the radius (r). The formula for relating radius and diameter is d=2r.

Formulas for the circle.

• The distance around the circle is called the circumference the formula is C = 2πr= πd.

• The area of a circle is A = πr2.

• π is the irrational number pi. An approximation for pi is 3.14 or the fraction 22/7.