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Area of Plane Shapes

  • The area of a shape is a measure of its surface.
  • Area is measured in units such as cm² or m², which are derived from the SI units of length.
  • The areas of common plane shapes are as follows:
    • Rectangle = L × B
    • Square = L²
    • Parallelogram = Base × Height
    • Triangle = ½ × Base × Height
    • Trapezium = ½ h(a + b)
    • Circle = πr²
Examples
  1. Calculate the area of a rectangle 6 cm by 3.5 cm.
    • Area of a rectangle = L × B
    • L = 6 cm
    • B = 3.5 cm
    • ∴ The area of the rectangle = 6 × 3.5
    • ∴ The area of the rectangle = 21 cm²
  2. The area of a rectangle is 224 cm². If its length is 16 cm, calculate the breadth.
    • Area of a rectangle = L × B
    • Area = 224 cm²
    • L = 16 cm
    • ∴ 224 = 16 × B
    • B = 224/16
    • ∴ Breadth of the rectangle = 14 cm²
  3. The area of a square plot is 144 m². Calculate the length of a side of the plot.
    • Area of a square = L²
    • Area = 144 m²
    • ∴ 144 = L²
    • ∴ L = √144
    • ∴ L = 12 m
  4. An assembly area is in the shape of a 30 m by 30 m square. Part of the area is a concrete rectangle 25 m by 5m, the rest is grass. Calculate the area of the grass.

    • Area of assembly area = L²
    •                                          = 30²
    • ∴ Area of assembly area = 900 m²
    • Area of concrete = L × B
    •                                = 25 × 5
    • ∴ Area of concrete = 125 m²
    • ∴ Area of grass = 900 – 125
    • ∴ Area of grass = 775 m²
  5. Calculate the area of a parallelogram if its base is 9.2 cm and its height is 6 cm.
    • Area of parallelogram = base × height
    •                                            = 9.2 × 6
    • ∴ Area of the Parallelogram = 55.2 cm²
  6. In the figure below, the base of the parallelogram is 6 cm and its height is 4 cm. Calculate the area of the parallelogram. If the length of the other side of the parallelogram is 8 cm, calculate the corresponding height, h.

    • Area of parallelogram = 6 × 4
    • ∴ The area of parallelogram = 24 cm²
    • Also, the area of the parallelogram = 8 × h
    • ∴ 24 = 8 × h
    • ∴ h = 24/8
    • ∴ The height = 3 cm
  7. Calculate the area of the triangle shown in the figure below.

    • Area of a triangle = ½ × B × H
    •                                      = ½ × 9 × 12
    • ∴ The area of the triangle = 54 cm²

  8. The diagonal AC divides the trapezium into two triangles. The height of each triangle is 8 cm. Calculate the area of the trapezium.

    • Area of Δ ACB = ½ × 13 × 8 = 52 cm²
    • Area of Δ ACB = ½ × 6 × 8 = 24 cm²
    • Area of trapezium = Area of Δ ACB + Area of Δ ACB
    •                                      = 52 + 24
    • ∴ The area of the trapezium = 76 cm²
  9. Find the area of a circle of radius 31/2 meters. (Let π = 22/7)
    • Area of a circle = πr²
    •                                 = 22/7 × (31/2
    •                                 = 22/7 × 7/2 × 7/2
    •                                 = 11/2 × 7
    •                                 = 77/2
    •                                 = 381/2
  10.   Calculate the area of the shape in the figure below. (Let π = 22/7). The radius of the semi-circle is 7 m.

    • Area of shape = Area of Big Rectangle + Area of Small Rectangle + Area of Semi Circle
    • Area of big rectangle = 16 × 10 = 160 m²
    • Area of small rectangle = 14 × 1 = 14 m²
    • Area of semi circle = ½ × 22/7 × 7 × 7 = 77 m²
    • ∴ The area of the shape = 160 + 14 + 77
    • ∴ The area of the shape = 251 m²
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