1. PERIMETER AND AREA PRESENTATION 4 - circles and π UNIT 4 MATHS

2. How are kites similar to rhombuses? How are rhombuses different to parallelograms? How are squares similar to rhombuses? How are kites similar to squares? How are kites different to squares? The number of equal sides; the number of opposite angles that are equal; and the lengths of the diagonals. review questions

3. How are kites similar to rhombuses? They both have adjacent sides equal and their diagonals intersect at right-angles. How are rhombuses different to parallelograms? A rhombus has a right-angle where the diagonals meet; all sides equal and diagonals bisect each other. Parallelograms don’t. How are squares similar to rhombuses? Both have four sides equal; two pairs of opposite sides are parallel; diagonals are perpendicular bisectors. How are kites similar to squares? Both have four sides (quadrilaterals); the diagonals intersect at right-angles. How are kites different to squares? The number of equal sides; the number of opposite angles that are equal; and the lengths of the diagonals. answers to review questions

4. HAVE A LOOK AT THESE CROSS SECTIONS OF ROCK HOW COULD YOU CALCULATE THE CIRCUMFERENCE AND AREA OF THESE SHAPES?

5. before we look at properties of circles have a look at the GREEK ALPHABET what is the 16th letter? this letter pi (π) is used as a symbol in circle geometry... - do you know what it means? - have you ever seen any other greek letters in maths or science?

6. The ancient Egyptians seem to have discovered that the circumference of a circle is approximately 3.14 times the diameter of the circle! they built the great pyramids using the ratio of 3.14 to 1 (circumference to diameter)

7. The perimeter of a circle is called the CIRCUMFERENCE:circle Radius, Diameter and Circumference and PI (π) The Radius is the distance from the center to the edge. The Diameter starts at one side of the circle, goes through the center and ends on the other side. The Circumference is the distance around the edge of the circle.

8. When you divide the circumference by the diameter you get 3.141592654... which is the number π (Pi)Pi So when the diameter is 1, the circumference is 3.141592654... (N.B. in maths and science we normally express numbers to 3 significant figures so π = 3.14) We can say: Circumference = π × Diameter Example: You walk around a circle which has a diameter of 100m, how far have you walked? Distance walked = Circumference = π × 100m = 314m (to the nearest m)

9. your turn! this circle has a diameter of 14 inches. what is its circumference? A 44 inches B 50 inches C 88 inches D 154 inches

10. (A) A circular pond has a radius of 10 feet. What is the circumference of the pond? Use 3.14 as an approximation for π A 314 feet B 157 feet C 62.8 feet D 31.4 feet (B) A circular garden has a radius of 21 m The owner wants to put a plastic edge around the garden, so wants to know what is the circumference of the garden? Use (22/7) as an approximation for π A 66 m B 132 m C 346.5 m D 1,386 m

11. the earth has a radius of approximately 20,035km at the equator and 20,004km through the poles Q: calculate the approximate circumference around (a) the equator (b) the poles

12. AREA OF CIRCLES The area of a circle is the number of square units inside that circle. If each square in the circle to the left has an area of 1 cm 2, you could count the total number of squares to get the area of this circle. Thus, if there were a total of 28.26 squares, the area of this circle would be 28.26 cm 2 However, it is easier to use the following formula: remember the value of π is 3.14 If a circle has a radius of 4, its area is 3.14 * 4 * 4 = 50.24 remember: If you know the diameter, the radius is 1/2 as large. πr²

13. Calculate the diameter or radius of each circle.

14. Calculate the diameter of each circle. Use pi=3.14 if needed. c = circumference

15. Calculate the area and circumference of each circle. Use pi=3.14.

16. Calculate the diameter of each circle. Use pi=3.14 if needed.