Perimeter, Circumference, and Area Sec. 1-9 Perimeter, Circumference, and Area Objective: Find the perimeters and areas of rectangles, squares, & the circumferences of circles.

Definitions Perimeter – Distance around a figure Sum of the lengths of its sides. Units are regular cm, in, ft Area – Is the number of square units a figure encloses. Units are squared cm2, in2, ft2

A = l x w A = b x h Square * 4 right angles * All 4 sides are congruent () Perimeter = sum of all 4 sides Ps = s + s + s + s Ps = 4s A = l x w A = b x h

Example: 1 A square has side with a length of 5cm. What is the perimeter and area of this square. *Draw and label a diagram first!! 5cm Ps = 4s Ps = 4(5cm) Ps = 20cm As = l x w As = 5cm x 5cm As = 25cm2

Example 2 The area of a square is 81cm2. How long is each of its sides. 81cm2 As = l x w As = s x s As = s2 81cm2 = s2 √81cm2 = √s2 9cm = s

Rectangles Two pairs of congruent sides. length Opposite sides are congruent 4 right angles PR = 2l + 2w A R = l x w length w w

Example 3: Rectangle Example 3: Find the perimeter and area of the following rectangle. 9m 12m PR = 2l + 2w PR = 2(12m) + 2(9m) PR = 24m + 18m PR =42m AR = l x w AR = 12m x 9m AR = 108m2

Quadrilateral ABCD has vertices A(0, 0), B(9, 12), C(11, 12), and D(2, 0). Find the perimeter. Draw and label ABCD on a coordinate plane. Find the length of each side. Add the lengths to find the perimeter. AB = (9 – 0)2 + (12 – 0)2 = 92 + 122 Use the Distance Formula. = 81 + 144 = 255 = 15 BC = |11 – 9| = |2| = 2 Ruler Postulate CD = (2 – 11)2 + (0 – 12)2 = (–9)2 + (–12)2Use the Distance Formula. = 81 + 144 = 255 = 15 1-7 DA = |2 – 0| = |2| = 2 Ruler Postulate

Perimeter = AB + BC + CD + DA (continued) Perimeter = AB + BC + CD + DA = 15 + 2 + 15 + 2 = 34 The perimeter of quadrilateral ABCD is 34 units. 1-7

Circles Circle – A set of points equal distance from a given point. * The given point is called the CENTER Radius- segment with endpoints at the center of the circle and on the circle. Diameter – Segment in a circle with endpoints on the circle and contains the center of the circle. r d 2r = d

Circles continued Circumference – Distance around the circle * The perimeter of the circle. C = d or C = 2r Area of a circle * How many square units inside the circle. * Units squared AC = r2

Example 4 3 Find the circumference and the area of a circle with a radius of 3ft. C = 2r C = 2(3ft) C = 6ft C = 18.8ft AC = r2 AC = (3ft)2 AC = 9ft2 AC = 28.3ft2

Example 5 & 6 The diameter of a circle is 16mm. Find its Circumference. C = 2r C = 2(8mm) C = 16mm C = 50.3mm The circumference of a circle is 28in. What is its radius? C = 2r 28in = 2r 2 2 r = 4.5in

Draw a horizontal line to separate the figure into three Find the area of the figure below. Draw a horizontal line to separate the figure into three nonoverlapping figures: a rectangle and two squares. 1-9

Find each area. Then add the areas. (continued) AR = bh Formula for area of a rectangle AR = (15)(5) Substitute 15 for b and 5 for h. AR = 75 AS = s2 Formula for area of a square AS = (5)2 Substitute 5 for s. AS = 25 A = 75 + 25 + 25 Add the areas. A = 125 The area of the figure is 125 ft2. -9

2 Postulates P(1-9) If 2 figures are congruent, then their areas are equal. II. P(1-10) The area of a region is the sum of the area of its nonoverlapping parts.

Example 7: Composite Figure Find the perimeter and area of the following figure. P = 16cm + 16cm + 8cm + 3cm + 3cm + 2cm P = 48cm

Example 7 continues: Area of composite figure A1 = l x w A1 = 8cm x 7cm A1 = 56cm2 A2 = l x w A2 = 5cm x 4cm A2 = 20cm2 A3 = l x w A3 = 2cm x 5cm A3 = 10cm2 AT = A1 + A2 +A3 AT = 56cm2 + 20cm2 +10cm2 AT = 86cm2

Ex.8: Find the Area of the following figure. Ab = l x w = 50in x 30in =150in2 As = l x w = 10in x 5in =50in2 At = Ab – As = 100in2