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## Perimeter and Area

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**Perimeter and Area**A look at a few basic shapes**This little square represents a bigger square, one yard in**length, and one yard in width.**110 yards**75 yards and 75 yards wide**110 yards**75 yards**110 yards**110 yards 75 yards 75 yards What is the perimeter of the football pitch?**110 yards**110 yards 75 yards 75 yards 110 + 75 + 110 + 75 = 370 yards**Our classroom is approximately**8 metres by 5 metres What is the perimeter?**8 m**Our classroom 5 m**8 m**8 m Our classroom 5 m 5 m 8 + 5 + 8 + 5 = 26 metres**Question?**How do we find the perimeter of a triangle? Answer: Let Google Maps do the measuring for us.**The perimeter of the Bermuda Triangle is approximately**4700 km**3 m**5 m 4 m The perimeter of this triangle? 3 + 4 + 5 = 12 metres**13 cm**5 cm 12 cm The perimeter of this triangle? 5 + 12 + 13 = 30 cm**These TETROMINOES are all made from four squares**Do they all have the same perimeter?**I get the following:**10 units 10 units 10 units 8 units 10 units**Pause for Play**Draw some shapes with a perimeter of 20 centimetres.**Let’s go back to Stamford Bridge**What is the perimeter of that circle in the middle? Actually, on a circle it is called the circumference**10 yards**According to BBC Sport, it has a radius of 10 yards. Which is from the centre of the circle to the circumference.**20 yards**10 yards If the radius is 10 yards, then the diameter is 20 yards. The circumference is about three times the diameter. So the circumference is about 3 x 20 = 60 yards**20 yards**60 yards**20 yards**10 yards If you have a calculator, then you could say it is 3.1, or 3.14, or 3.142 times the diameter. If you have a posh calculator, you could use the πbutton.**Pi – the Greek letter π, which represents the ratio of**the circumference to the diameter of a circle. • We can’t actually write it down exactly. • But we can write it to as many decimal places as we want.**If you have a computer you could use a thousand decimal**places…**3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019…**3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019…**Pause for Play**6 cm 4 cm Which has the greatest perimeter? 8 cm 8 cm**Area**Return to the classroom**5 m**8 m What do we use to measure area?**Square metres**(or square yards, or square inches, or square centimetres…)**8 m**How many square metres? 5 m**8 m**5 m 5 x 8 = 40 square metres, or 40 m2**Pause for Play**Draw some rectangles with an area of 20 square centimetres. Do they have the same perimeter?**110 yards**75 yards What, in square yards, is the area of Stamford Bridge?**110 yards**75 yards 110 x 75 = 8250 square yards**5 cm**12 cm Start with a simple one:**What if we ‘double up’?**5 cm 12 cm**5 cm**12 cm Area of the rectangle? Area of the triangle?**5 cm**12 cm Area of the rectangle = 60 cm2 Area of the triangle = 30 cm2**3 cm**8 cm Slightly more complicated:**8 cm**But we can still ‘double up’ 3 cm**3 cm**8 cm Area of rectangle = 3 x 8 = 24 Area of triangle = (3 x 8) ÷ 2 = 12 cm2