How To Find The Area AND Perimeter Of a Regular Flatlander A Geometry project by Drew Rio Kurt Brad To learn about finding perimeter and area, click here To take the quiz, click here To See Formulas, click here

Formulas Area Formulas Triangle - A= 1/2 bh Square – A = bh Pentagon – A= 1/2ap Octagon-A= 1/2ap Circle-A=  r 2 More Info

Formulas Cont. Other Formulas Pythagorean Theorem - a 2 + b 2 = c 2 Perimeter (Circumference) of a Circle-2  r Back

Finding Perimeter of Any Regular Flatlander To find the perimeter of a regular add the measure of all the sides together Example P = length of sides ∙ # of sides P = 4 ∙ 3 P = 12

Finding the Area of an Equilateral Triangle (Tradesmen) Make an altitude from the vertex to the base. Then, divide the measure of the base by two. (It has been bisected so it is half the size) Next, use the Pythagorean Theorem to find the height of the triangle. Then multiply the base by the height, Then divide by two Example A = 1/2bh A = 1/2(4)(3.46) A =6.92

Finding the Area of a Square (Gentlemen) Multiply the measure of the base by the measure of the height Example A = s 2 A = 4 2 A = 16

Finding the Area of a Regular Pentagon (Gentlemen) To find the area of a regular pentagon use the apothem and multiply it by the perimeter of the figure. Example A = 1/2ap A = 1/2(4)(30) A = 60

Finding The Area of A Hexagon Find the perimeter of the hexagon Multiply by the apothem Divide by 2 Example A = 1/2ap A = 1/2(5)(36) A = 90 6

Finding The Area Of a Regular Octagon (Nobility) Find the perimeter of the octagon Multiply the perimeter by the apothem Example P = length of sides ∙ # of sides P = 6 ∙ 8 P = 48 A=1/2ap A=1/2 8*48 A=192

Finding The Circumference of a Circle (Priestly) Multiply the radius by Pi (3.14) Example- 6 C = 2 πr C = 2(3.14)(6) C = 18.84*2 C=37.68

Finding the Area of A Circle First, multiply the radius by itself. Multiply the product by Pi (3.14) Example- 6 A = πr 2 A = (3.14)(6) 2 A = (3.14)(36) A =

QUIZ 1) What does regular mean when you say regular pentagon? 2) Find the area of this regular flatlander. 4

Answers 1) It means that all of the sides are congruent, and all of the angles are congruent. 4cm 2) 4cm 4cm find the height by using the Pythagorean Theorem, then the multiply the base by the height and divide by 2 H=3.46 A=13.85

Questions 3) What is the formula to find the area of a triangle? 4) Find the area of this square. 5cm

Answers 3) What is the formula to find the area of a triangle? A=1/2bh 4) Find the area of this square. 25 cm 2 5cm

Questions 5) Find the area of this circle? 6) What is the formula for the area of a circle. 5

Answers 5) Find the area of this circle? ) What is the formula for the area of a circle. A=  r 2 5

Questions 7) Find the perimeter of this square. 8) Find the perimeter of this pentagon 4 3

Answers 7) P=16 8)P=15

Questions 9) Find the Perimeter of this hexagon 10) What is the perimeter formula? 8

Answers 9) P=48 10) P= length of sides times number of sides

YOU’RE DONE Thank you for Visiting!