Saturday X-tra X-Sheet: 12. Revision of Grade 12 Space and Shape Part 1 2D Shapes

Transcription

1 Saturday X-tra X-Sheet: 12 Key Concepts Revision of Grade 12 Space and Shape Part 1 2D Shapes In this session we will focus on summarising what you need to know about: Measurement conversions of units of length Area Perimeter Terminology & definitions Measurements and conversions. You need to know: LENGTHS 1 cm = 10 mm 1m = 100cm = 1000mm 1km = 1000m = cm = mm 1cm 2 = 100mm 2 1cm 10mm 1 cm 2 1cm = 100mm 2 10mm 1m 2 = cm 2 = mm 2 1 m 100 cm 1000mm 1 m 1m 2 2 = cm 2 = cm mm mm 2 2 1m cm 1000mm 1km 2 = m 2 = cm 2 Units of measurement can be converted from metric to imperial units and imperial to metric units. You do not have to learn these conversions the conversion amounts will be given to you. Area = the amount of space that the surface of a place or shape covers. Area is expressed in square units, such as square metres. Perimeter = the total length of the sides of a shape. Circumference = the distance around the edge of a circle. Page 1

2 Area and perimeters of common shapes: Square Side Area = side x side Side Perimeter = side x 4 Rectangle breadth length Area = length x breadth Perimeter = 2 x (length + breadth) Triangle height Area = ½ base x height Perimeter = add 3 sides base Parallelogram height Area = base x height Perimeter = add 4 sides Base Trapezium a height Area = (top + bottom) 2 x height OR = (a + b) 2 x height Perimeter = add 4 sides b Circle Radius Radius = ½ diameter Area = = Circumference (perimeter) =2 חx x radius OR C ח= x diameter Page 2

3 Pythagoras RIGHT ANGLED TRIANGLES ONLY Short side 1 hypotenuse Short side 2 Hypotenuse 2 = (short side 1) 2 + (short side 2) 2 Hypotenuse = (short side 1) 2 + (short side 2) 2 Short side 1 = (hypotenuse) 2 - (short side 2) 2 Short side 2 = (hypotenuse) 2 - (short side 1) 2 Concept: Measurement - lengths and areas X-ample 1: 2,3 m = cm X-ample 2: m = km X-ample 3: 2,3m 2 = cm 2 X-ample cm 2 = m 2 X-ample 5 1 foot = 30cm I measure the length of the desk to be 7 feet. Convert this to metres. X-ample 6 1 m = 3,25 feet I measure the length of a container. The length is 3,5 m. I need to send the measurements to an English company that uses imperial units. Convert this measurement from metres to feet. Page 3

4 X-ample 7 Write the ratio of 2,2km to 11m in its simplest form. Concept: Area and perimeter X-ample 8: Find the area and the perimeter of this shape. X-ample 9 Find the shaded area of this shape. Use = where = 3,14. Give your answer to 1 d.p. 8,6 cm 3,1 cm Page 4

5 X-ample 10 Mr Brown, the gardener at school, created a circular flower-bed in a rectangular lawn, as seen in the diagram. The radius of the flower-bed is 1,5m. The length of the rectangular lawn is 6m and the breadth is 4m. Calculate the following: a. The area of the flower bed. Use the formula: Area = ח x radius 2, where ח = 3,14 b. The perimeter of the lawn. Use the formula: Perimeter= 2 (length + breadth) c. The length of the lawn in feet if 1m = 3,25 feet. X-ample 11 2m Find the area of the shape in m cm Page 5

6 X-ample 12 Area Find the area of the shaded part, if the radius of the circle is 15cm. Let =3,14. 40cm 20cm X-ample 13 Look at the shape below: a. Find the length of one of the sides of the square. b. Use this information to find the area of the whole shape. c. Find the perimeter of the shape. (not the dotted line.) X-ample 14 Measurement 1. Write the ratio of 2 km to m in simplified form. 2. 2,3m = cm m = km mm 2 = cm 2 5. Convert 2,3 inches to cm. If 1 inch = 2,5cm. Page 6

7 X-ercise Measurement 1. Write the ratio of 5 km to 2 50 m in simplified form. 2. 0,03m = cm m = km mm 2 = cm 2 5. Convert 1,7 inches to cm. If 1 inch = 2,5cm. Area 1. A worker is employed to make triangular bandanas, as shown by the rightangled triangle ABC in the diagram below. A 300mm B 400mm C a. Calculate the area, in square metres, of one bandana. b. Calculate the length, in metres, of diagonal AC of the bandana. c. The worker would like to put fancy edging on the bandana. Calculate the total length of edging, in metres, that would be required per bandana. Page 7

8 2. Josie wants to install wood flooring in her loft area. She makes the following diagram to take to Makro: 620cm 255cm 360cm A B 340cm a. Calculate the lengths of the missing sides A and B. b. Calculate the area of the room in cm 2 and m 2. c. One box of wood flooring covers an area of 7m 2. How many boxes will she need to purchase? d. How much extra flooring material would be left over? 3. Find the shaded area of this shape. Use = where = 3,14. Give your answer to 1 d.p. R = 5cm r = 3cm Page 8

9 X-ercise Answers: Measurement 1. 20:1 2. 0,03m = 30cm m = 20,250km mm 2 = cm ,25 cm Area 1. a. Area = ½ (0.4 x 0.3) = 0,06m 2 b. Length of diagonal = 0,4 +0,3 = 0,5m c. Perimeter = 0,4 + 0,3 + 0,5 = 1,2m 2. a. A = 280cm and B = 105cm b. Area = (620 x 255) + (105 x 340) = cm 2 Area = (6,2 x 2,55) + (1,05 x 3,4) = 19,38m 2 c. No. Boxes = 19,38 7 = 2,7685 boxes rounded to 3 boxes d. 3 boxes = 21m 2 Amount of flooring left over = 21 19,38 = 1,62m 2 3. Area of shaded part = Rח 2 - rח 2 = (3,14 x 5 2 ) (3,14 x 3 2 ) = 50,2cm 2 (1.d.p) Page 9