Length and Area (Quadrilaterals and Circles) Vocabulary: Circle Sector Radius Diameter Circumference Tangent Segment chord Parallelogram Rhombus Kite perimeter quadrant Area exact approximate Semicircle dimensions arc Trapezium

What do you remember… How do you find the perimeter of a figure? What is the formula for finding the area of a: Rectangle Square Triangle?

Revision:

Find the area AND the perimeter of each shape:

Area of a parallelogram We can find the area of a parallelogram by cutting it and rearranging the pieces: Demonstration So the area of a parallelogram is found using: Area = base x height A = b x h = 5 x 12 = 60 cm2

Areas of other special Quadrilaterals

Challenge!

Properties of a Circle A circle is defined as a set of points which is equally distant (or equidistant) from one fixed point. The fixed point is called the centre of the circle. The line joining the centre to the circumference is called the radius The diameter goes through the centre, from one side of the circle to the other. It is twice as long as the radius A chord joins any two points on the circumference. A chord divides a circle into a major segment and a minor segment

Labelling Activity:

tangent

Identify each feature:

Investigation: Draw EIGHT different sized circles (carefully) using a pair of compasses in your book. Use the string to measure the circumference (around the edge) and record it in a table like below. Measure and record the diameter (distance across the circle) of each circle. Circumference Diameter

What is ?

Circumference of a Circle The circumference of any circle is given by: You use the most appropriate formula, depending on whether you know the radius or the diameter. Who can remember the most digits of ?

What about parts of a circle’s circumference? In general terms:

Challenge!

Area of a Circle We can use what we know about the circumference of a circle to find the area of the circle… So the area of a circle is A = r2 where r is the radius

Applications