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Math Challenges: Metric Conversion & Geometric Shapes Exploration

Dive into metric conversion, perimeter, area of shapes like parallelograms, trapezoids, circles, and complex shapes. Solve challenging problems and calculate circumferences, areas, and perimeters using formulas. Explore geometric concepts step by step.

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Math Challenges: Metric Conversion & Geometric Shapes Exploration

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  1. Measurement Grade 6 L.G: Metric Conversion, Perimeter and area of parallelograms, and complex shapes Grade 7 L.G: Metric Conversion, Perimeter and area of trapezoids, and complex shapes Grade 8 L.G: Metric Conversion, Circumference and area of circles, and complex shapes

  2. You Try! 1 11230 • 1000 m = _____ km • 903 cm = _____ m • 40 dm = _____ cm • 959 mm = ______ m • 8.13 m = ______ cm • 11.23 L = ______ mL • 0.09 m = _____ cm • 45.09cm = _____ dam • 11m2 = _____ cm2 • 25cm2= _______ m2 9.03 9 0.04509 400 0.959 110000 0.001025 813

  3. Rectangles Sum of interior angles = 360° Perimeter = 5cm + 5cm + 8cm + 8cm = 26cm Area = (Length)(Width) = (5cm)(8cm) = 40cm²

  4. Triangles Sum of interior angles = 180°

  5. Right Angle Triangles

  6. Area and Perimeter of Triangles Perimeter = 15cm + 6cm + 8cm = 29cm Area = (base)(height) 2 = (8cm)(5cm) 2 = 20cm²

  7. Parallelograms Quadrilateral with opposite sides parallel

  8. Area and Perimeter of Parallelograms Perimeter = 2m + 2m + 2.5m + 2.5m = 9m Area = Area Triangle 1 + Area Triangle 2 = (base)(height) + (base)(height) 2 2 = (base)(height) = (2.5m) (1.8m) = 4.5m²

  9. Trapezoids Quadrilateral with 1 set of opposite sides parallel

  10. Area and Perimeter of Trapezoids Perimeter = 12mm + 14mm + 18mm + 13mm = 57mm Area = Area Triangle 1 + Area Triangle 2 = (base)(height) + (base)(height) 2 2 = (height) (base 1 + base 2) 2 = (11mm) (12mm + 18mm) 2 = (5.5mm) (30mm) = 165mm²

  11. Circles

  12. Circles Circumference = 15cm Diameter = 4.774cm Circumference : Diameter 3.14 (pi) 3.141592653590 (never ends and never repeats) **When calculating, round to 3.1416 **

  13. Finding the Circumference of a Circle = = = = r = 2 (5m) = 2 (3.1416)(5m) = 31.416m

  14. Finding the Radius of a Circle = = radius = circumference 2 r= = 50mm/2 = 50mm/2(3.1416) = 7.9577mm

  15. Area of a Circle

  16. Area of a Circle = ² = 78.54m²

  17. Area of Complex Shapes **To find the area of complex shapes, break them up into simpler shapes. Find each area and add them together** Area = A(triangle) + A(trapezoid) = bh + h (base 1 + base 2) 2 2 = (15m)(7m)+ 8m (24m + 15m) 2 2 = 105m² + 4m (39m) 2 = 52.5m² + 156m² = 208.5m²

  18. Area of Complex Shapes Area of complex shape = Total area – Inside area = (16m)(10m) – (12m)(6m) = 160m² - 72m² = 88m² 12m 6m

  19. Area of Complex Shapes Area = (Area square – Area Circle) + Area Triangle 2 = (20cm x20cm) - ² + (20cm)(20cm) 2 2 = 400cm² - 314.16cm² + 200cm² 2 = 42.92cm² + 200cm² = 242.92cm² 30cm

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