Geometry - Calculating Area and Perimeter

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1 Geometry - Calculating Area and Perimeter In order to complete any of mechanical trades assessments, you will need to memorize certain formulas. These are listed below: (The formulas for circle geometry will be given) Area of a square = s 1 Area of a triangle = b h Area of a rectangle = or b h l w Area of a cube = area of one face x number of faces *NOTE* The symbol means multiply, so l w is same as saying l x w Area (Polygons) A polygon is a geometric figure with 3 or more sides. The area of a polygon is number of squares (of a particular unit) that it takes to cover surface of shape. Formulae are used to calculate area. Example 1: Find area of a triangle which has a base of 10 mm and a height of 9 mm. A = 1 A = 1 b x h (10 mm x 9 mm) A = 1 (90 mm ) A = 45 mm Example : Find area of a square that has a side with a length of 6 cm. or b x h A 10 mm x 9 mm A 90 mm A A 45 mm A = s A = (6 cm) A = 36 cm Example 3: Find area of a rectangle that has a length of 3.7 m and a width of.4 m. A = l x w A = (3.7 m) x (.4 m) A = 8.88 m Mechanical Trades: Area, Perimeter and Volume Study Guide 4 FB/015 Page 1

2 PRACTICE Find area of following shapes: a) b) c) 5 cm 10 cm 1.6 m 3 cm 5 cm d) e) 1 cm.3 ft uote 11 cm from Note: There are no diagrams for f) to h). docum f) A square 35 ft on a side. ent or g) A rectangle with length of 8.8 m and width of 4. m. h) A triangle with height of 9 km and base of 5. km. summa ry of * Tip* If you are asked to find area of an unusual shape, break it down into shapes that you an recognize. For example, if you were asked to find area of shape below, find area of interest triangle (roof) and n house (rectangle). When you add areas toger, you will have ing total area. point. You can positio n ANSWERS box a) 15 cm b) 5 cm c) m d) 11 cm e) anywh 5.9 ft f) 15 ft g) m h) 3.4 km ere in docum ent. Use Drawi ng Tools tab to change Mechanical Trades: Area, Perimeter and Volume Study Guide 4 FB/015 formatt Page ing of text

3 Circle Geometry Circumference is name for perimeter (or distance around outside) of a circle. In this circle, centre is Z. A, B, and C are points on circle. Radius: The distance from centre of circle to any point on circle is called radius (r). (ZA is a radius. ZB and ZC are too). Diameter: The distance from any point on circle, passing through centrepoint and continuing on to outer edge of circle (d). (AB is diameter of circle to right.) To find circumference (or perimeter) of circle, use one of following formulae: (1) C = π d OR () C = π r π is called pi and is about 3.14 or 7 Example A: If circle has a radius of 5 cm, n (1) C =π d () C = π r The diameter would be twice radius (or 5 cm x = 10 cm) C = (3.14) (10 cm) C = 31.4 cm. The radius is 5 cm So C = () (3.14) (5) C = 31.4 cm Both formulae work equally well. You may choose eir one. Now let's practice: 1. A circle has a diameter of 0 m. What is circumference?. A circle has a radius of 7 km. What is circumference? 3. Find circumference for following circles: a) radius(r) = 14 cm (use π = 3.14 or ) 7 b) diameter (d) = 60 mm c) radius (r) = 15 m ANSWERS - Please note that answers may vary depending on value used for π (Pi) 1) C = π d ; C = (3.14)(0); C = 6.8 m ) C = π r; C = ()(3.14)(7); C = km b) C = π d ; C = 3.14(60) = mm 3) a) C = π r; C = () (14) = 88 cm 7 c) C = π r ; C = ()(3.14)(15); C = 94. m Mechanical Trades: Area, Perimeter and Volume Study Guide 4 FB/015 Page 3

4 Area (Circles) To find area of a circle, use formula A =π r A = area of circle: π = pi 3.14 or r = radius of circle 7 so A = π r A = 3.14 x (10) A = 3.14 x 100 A = 314 cm r = radius of circle = 10 cm *notice: answers are units Now let s practice: A: Find circumference and area of following circles: (1) radius = 4 km () diameter = 10 m B: Find circumference and area of following circles: (1) radius = 14 in. () diameter = 0 mm ANSWERS - - Please note that answers may vary depending on value used for π (Pi) A: 1) C = π r; C = (3.14)(4): C = 5.1 km A = π r A = (3.14)( 4) = 50.4 km ) C= π d ; C = (3.14)(10); C = 31.4m A = π r A = (3.14)(5) = 78.5 m B: 3) C = π r; C = ( 3.14)( 14) = 87.9 in A = π r A = (3.14)(14) = in 4) C= π d ; C = (3.14)(0) = 6.8 mm A = π r A = (3.14)(10) = 314 mm Mechanical Trades: Area, Perimeter and Volume Study Guide 4 FB/015 Page 4

5 Perimeter The perimeter of a polygon is distance around outside of figure, or sum of length of each of its sides. Sometimes formulae are used in calculating perimeter to make things easier. The most common formulae used are as follows: Perimeter of a Rectangle or a Parallelogram: P = (l + w) or P = l + w Perimeter of a Square: P = 4 s Example 1: Find perimeter of a rectangle that is 6 mm by 9 mm P = 6 mm + 6 mm + 9 mm + 9mm = 30 mm or P = l + w = (9 mm) + (6 mm) = 18 mm + 1 mm = 30 mm or P = (l + w) = (6 mm + 9 mm) = (15 mm) = 30 mm Example : Find perimeter of a square with a side that is 10 cm long P = 10 cm + 10 cm + 10 cm + 10 cm = 40 cm or P = 4s = 4 (10 cm) = 40 cm Example 3: Find perimeter of a parallelogram that has a length of 1m and a width of 5m P = (l + w) = (1 m + 5 m) = (17 m) = 34 m or P = / + w = (1 m) + (5 m) = 4 m + 10 m = 34 m or P = 5 m + 1 m + 5 m + 1 m = 34 m Mechanical Trades: Area, Perimeter and Volume Study Guide 4 FB/015 Page 5

6 PRACTICE Find perimeter of following shapes: Mechanical Trades: Area, Perimeter and Volume Study Guide 4 FB/015 Page 6

7 ANSWERS a) 30 m b) 17 cm c) 0 m d) 8 mm e) 54.8 in f) 44 cm g) 67. ft h) 3.4 m i) 48 ft j) 47 ft k) 1 km l) 66.6 ft m) cm n) 510 m ** When converting a squared or cubed number be careful! To convert cm to m, we divide by 100 and 100 again To convert cm 3 to m 3, we divide by 100 n anor hundred and n a third hundred To convert square inches to square feet, we divide by 1 and n 1 again To convert cubed inches to cubed feet, we divide by 1 (three times) Mechanical Trades: Area, Perimeter and Volume Study Guide 4 FB/015 Page 7

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