#### 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__

__Examples__

- 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

- 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

- 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

- 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

- 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

- 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

- 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

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

- Find the area of a circle of radius 3
^{1}/_{2}meters. (Let π =^{22}/_{7})- Area of a circle = πr²
- =
^{22}/_{7 }× (3^{1}/_{2})² - =
^{22}/_{7 }×^{7}/_{2}×^{7}/_{2} - =
^{11}/_{2}× 7 - =
^{77}/_{2} - = 38
^{1}/_{2}m²

- 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