Comprehensive formula sheet for calculating the area of various 2D shapes, featuring diagrams and mathematical equations.

The image provided is a formula sheet for calculating the areas of various 2D shapes. Below, I will explain each shape and its corresponding area formula:

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1. Square

- Shape: A square has four equal sides and four right angles.
- Formula for Area:
\[
\text{Area} = \text{Base} \times \text{Height}
\]
Since all sides are equal in a square, the base and height are the same. Therefore, the formula can also be written as:
\[
\text{Area} = \text{Side}^2
\]

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2. Rectangle

- Shape: A rectangle has opposite sides that are equal and four right angles.
- Formula for Area:
\[
\text{Area} = \text{Base} \times \text{Height}
\]
Here, the base and height are the lengths of the two adjacent sides.

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3. Triangle

- Shape: A triangle has three sides.
- Formula for Area:
\[
\text{Area} = \frac{\text{Base} \times \text{Perpendicular Height}}{2}
\]
The perpendicular height is the distance from the base to the opposite vertex (height measured perpendicularly).

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4. Trapezium

- Shape: A trapezium has one pair of parallel sides.
- Formula for Area:
\[
\text{Area} = \frac{(\text{a} + \text{b}) \times \text{Height}}{2}
\]
Here, \( \text{a} \) and \( \text{b} \) are the lengths of the two parallel sides, and the height is the perpendicular distance between these parallel sides.

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5. Parallelogram

- Shape: A parallelogram has opposite sides that are equal and parallel.
- Formula for Area:
\[
\text{Area} = \text{Base} \times \text{Perpendicular Height}
\]
The perpendicular height is the distance from the base to the opposite side, measured perpendicularly.

---

6. Rhombus

- Shape: A rhombus has four equal sides and opposite angles that are equal.
- Formula for Area:
\[
\text{Area} = \frac{\text{Length} \times \text{Height}}{2}
\]
Here, the length refers to the diagonal of the rhombus, and the height is the perpendicular distance between the diagonals.

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7. Kite

- Shape: A kite has two pairs of adjacent sides that are equal.
- Formula for Area:
\[
\text{Area} = \frac{\text{Length} \times \text{Height}}{2}
\]
Similar to the rhombus, the length refers to the diagonal, and the height is the perpendicular distance between the diagonals.

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Summary of Formulas

1. Square: \( \text{Area} = \text{Side}^2 \)
2. Rectangle: \( \text{Area} = \text{Base} \times \text{Height} \)
3. Triangle: \( \text{Area} = \frac{\text{Base} \times \text{Height}}{2} \)
4. Trapezium: \( \text{Area} = \frac{(\text{a} + \text{b}) \times \text{Height}}{2} \)
5. Parallelogram: \( \text{Area} = \text{Base} \times \text{Height} \)
6. Rhombus: \( \text{Area} = \frac{\text{Diagonal}_1 \times \text{Diagonal}_2}{2} \)
7. Kite: \( \text{Area} = \frac{\text{Diagonal}_1 \times \text{Diagonal}_2}{2} \)

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These formulas are essential for calculating the areas of different 2D shapes. Each formula is derived based on the geometric properties of the shape.

Final Answer:
\[
\boxed{
\begin{aligned}
1. & \text{ Square: } \text{Area} = \text{Side}^2 \\
2. & \text{ Rectangle: } \text{Area} = \text{Base} \times \text{Height} \\
3. & \text{ Triangle: } \text{Area} = \frac{\text{Base} \times \text{Height}}{2} \\
4. & \text{ Trapezium: } \text{Area} = \frac{(\text{a} + \text{b}) \times \text{Height}}{2} \\
5. & \text{ Parallelogram: } \text{Area} = \text{Base} \times \text{Height} \\
6. & \text{ Rhombus: } \text{Area} = \frac{\text{Diagonal}_1 \times \text{Diagonal}_2}{2} \\
7. & \text{ Kite: } \text{Area} = \frac{\text{Diagonal}_1 \times \text{Diagonal}_2}{2}
\end{aligned}
}
\]