Worksheets for GCSE Mathematics. Perimeter & Area. Mr Black's Maths Resources for Teachers GCSE 1-9. Shape

Transcription

1 Worksheets for GCSE Mathematics Perimeter & Area Mr Black's Maths Resources for Teachers GCSE 1-9 Shape

2 Perimeter & Area Worksheets Contents Differentiated Independent Learning Worksheets Perimeter of Shapes Page 20 Area of Rectangles Page 30 Area of Irregular Shapes Page 40 Area of Triangles Page 50 Area of Parallelograms and Trapezia Page 60 Area of Compound Shapes Page 70 Circumference of Circular Shapes Page 80 Area of Circular Shapes Page 90 Arc Length of a Sector Page 10 Area of a Sector Page 11 Manipulating Sector s Formulae Page 12 Solutions Perimeter of Shapes Page 13 Area of Rectangles Page 13 Area of Irregular Shapes Page 14 Area of Triangles Page 14 Area of Parallelograms and Trapezia Page 15 Area of Compound Shapes Page 15 Circumference of Circular Shapes Page 16 Area of Circular Shapes Page 16 Arc Length of a Sector Page 17 Area of a Sector Page 17 Manipulating Sector s Formulae Page 17

3 Perimeter of Shapes Measure the perimeter around each of these shapes. Calculate the perimeter around each of these shapes. Q3. Calculate the perimeter of this compound shape. 2

4 Measure the area of these rectangles. Area of Rectangles Calculate the area of these rectangles Q3. Calculate the area of these rectangular shapes: Q4. Investigate the largest and smallest perimeter that can be made with a rectangle of area 36cm 2. 3

5 Area of Irregular Shapes Measure the area of these shapes by counting the squares inside. a) b) c) d) Measure the area of these objects by counting the squares inside. 4

6 Measure the area of each triangle. Area of Triangles Calculate the area of each triangle. Q3. Calculate the area of each triangle. Q4. Calculate the area of the shaded regions. 5

7 Parallelograms & Trapeziums Determine the area of these parallelograms and trapezia. Calculate the area of these parallelograms and trapezia. Q3. Calculate the values of the shaded areas. 6

8 Area of Compound Shapes Determine the area of these compound shapes. Calculate the area of these compound shapes. 7

9 Circumference of Circular Shapes Calculate the circumference of these circles, round your answers to 2 decimal places. Calculate the perimeter of these semi and quarter circles, round your answers to 2 decimal places. Q3. Calculate the perimeter of these shapes, round your answers to 2 decimal places. 8

10 Area of Circular Shapes Calculate the area of these circles, round your answers to 2 decimal places. Calculate the area of these semi and quarter circles, round your answers to 2 decimal places. Q3. Calculate the area of the shaded regions, round your answers to 2 decimal places. 9

11 Arc Length of Sectors Calculate the arc length of each sector. Calculate the perimeter of each shape. 10

12 Area of Sectors Calculate the area of these sectors, round your answer to 2 decimal places. Calculate the area of the shaded regions, round your answer to 2 decimal places. 11

13 Sectors Formulae Calculate the value of the unknown dimension using the formula for the arc length of a sector. Round your answer to three significant figures. Calculate the value of the unknown dimension using the formula for the arc area of a sector. Round your answer to three significant figures. 12

14 Perimeter Solutions a) 16 units b) 14 units c) 12 units d) 18 units e) 18 units f) 25 units g) 24 units h) 30 units a) 12 cm b) 14 cm c) 14 mm d) 18 cm e) 25 cm f) 24 cm g) 10 cm h) 38 m Q3. Perimeter = 80 cm Area of Rectangles Solutions a) 15 units 2 b) 14 units 2 c) 16 units 2 d) 8 units 2 e) 12 units 2 f) 10 units 2 a) 15 cm 2 b) 24 cm 2 c) 6 cm 2 d) 5 cm 2 e) 42 cm 2 f) 40 cm 2 Q3. a) Area = 22 cm 2 b) Area = 22 cm 2 13

15 Area of Irregular Shapes Solutions Q1a) Approximate Area = units 2 Q1b) Approximate Area = 7-9 units 2 Q1c) Approximate Area = units 2 Q1d) Approximate Area = units 2 Approximate Area for Owl = units 2 Approximate Area for Butterfly = units 2 Approximate Area for Cone = units 2 Area of Triangles Solutions a) 8 units 2 b) 9 units 2 c) 4.5 units 2 d) 7.5 units 2 a) 6 cm 2 b) 12 cm 2 c) 20 cm 2 d) 5 cm 2 e) 20 cm 2 f) 50 cm 2 g) 48 cm 2 h) 8 cm 2 Q3. a) 20 cm 2 b) 35 cm 2 c) 12 cm 2 d) 7.5 cm 2 Q4. a) Shaded Area = 57 m 2 b) Shaded Area = 81 m 2 14

16 Area of Parallelograms and Trapeziums Solutions a) 15 units 2 b) 12 units 2 c) 30 units 2 d) 20 units 2 e) 20 units 2 f) 17.5 units 2 g) 20 units 2 h) 20 units 2 a) 48 cm 2 b) 30 cm 2 c) 108 m 2 d) 10 m 2 e) 37.5 cm 2 f) 72 cm 2 g) 135 cm 2 h) 20 m 2 Q3. a) Shaded Area = 49.5 cm 2 b) Shaded Area = 39 m 2 Area of Compound Shapes Solutions a) 16 units 2 b) 18 units 2 c) 21 units 2 d) 12 units 2 e) 12 units 2 f) 27 units 2 g) 27 units 2 a) 21 cm 2 b) 16 cm 2 c) 76 m 2 d) 168 cm 2 e) 84 m 2 f) 126 m 2 g) 31 cm 2 h) 72 cm 2 i) 144 m 2 15

17 Circumference of Circular Shapes Solutions a) cm b) 37.7 m c) cm d) cm e) 9.43 mm f) 3.14m g) m h) m a) cm b) cm c) cm d) 9 cm e) 7.14 mm f) 5.36 m g) 25 m h) m Q3. a) Perimeter = cm b) Perimeter = cm c) Perimeter = cm Area of Circular Shapes Solutions a) cm 2 b) m 2 c) cm 2 d) cm 2 e) mm 2 f) 3.14 m 2 g) mm 2 h) mm 2 a) 6.29 cm 2 b) 9.82 cm 2 c) 6.29 cm 2 d) m 2 e) 7.07 cm 2 f) 0.79 m 2 g) m 2 h) m 2 Q3. a) Shaded Area = 7.72 cm 2 b) Shaded Area = cm 2 c) Shaded Area = cm 2 16

18 Arc Lengths of Sectors Solutions a) 1.57 cm b) 9.6 cm c) 7.86 cm d) 2.09 m e) mm f) 5.87 m g) cm h) mm a) Perimeter = cm b) Perimeter cm c) Perimeter = cm d) Perimeter = cm Area of Sectors Solutions a) 6.28cm 2 b) 1.96 cm 2 c) 2.98 m 2 d) m 2 e) m 2 f) mm 2 g) 0.46 m 2 h) mm 2 i) m 2 j) cm 2 a) Shaded Area = cm 2 b) Shaded Area = 3.24 m 2 c) Shaded Area = m 2 Sectors Formulae Solutions a) Radius = 6.87cm b) Radius = 14.3 cm c) Angle = 76.4 d) Radius = 7.16 cm e) Angle = 93.1 f) Angle = 78.8 a) Radius = 8.74cm b) Angle = 45.8 c) Radius = 7.57 m d) Angle = 84.9 e) Area = 18.9 m 2 f) Area = 41.9cm 2 17