Area & Perimeter formulas for common geometric shapes, illustrated with diagrams and equations.

The image provides formulas for calculating the area and perimeter of various geometric shapes. Below, I will explain each formula in detail:

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1. Rectangle

- Area (A): \( A = l \times w \)
- The area of a rectangle is calculated by multiplying its length (\( l \)) by its width (\( w \)).
- Perimeter (P): \( P = 2 \times (l + w) \)
- The perimeter is the total distance around the rectangle, calculated by adding the lengths of all four sides.

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2. Square

- Area (A): \( A = s^2 \)
- Since all sides of a square are equal, the area is the side length (\( s \)) squared.
- Perimeter (P): \( P = 4 \times s \)
- The perimeter is four times the side length (\( s \)).

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3. Triangle

- Area (A): \( A = \frac{b \times h}{2} \)
- The area of a triangle is half the product of its base (\( b \)) and height (\( h \)).
- Perimeter (P): \( P = s_1 + s_2 + s_3 \)
- The perimeter is the sum of the lengths of all three sides (\( s_1, s_2, s_3 \)).

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4. Parallelogram

- Area (A): \( A = b \times h \)
- The area is the product of the base (\( b \)) and the height (\( h \)).
- Perimeter (P): \( P = 2 \times (l + w) \)
- The perimeter is twice the sum of the lengths of adjacent sides (\( l \) and \( w \)).

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5. Trapezium

- Area (A): \( A = \frac{(a + b) \times h}{2} \)
- The area is half the product of the sum of the parallel sides (\( a \) and \( b \)) and the height (\( h \)).
- Perimeter (P): \( P = a + b + c + d \)
- The perimeter is the sum of the lengths of all four sides (\( a, b, c, d \)).

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6. Rhombus

- Area (A): \( A = \frac{d_1 \times d_2}{2} \)
- The area is half the product of the diagonals (\( d_1 \) and \( d_2 \)).
- Perimeter (P): \( P = 4 \times s \)
- All sides of a rhombus are equal, so the perimeter is four times the side length (\( s \)).

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7. Kite

- Area (A): \( A = \frac{d_1 \times d_2}{2} \)
- The area is half the product of the diagonals (\( d_1 \) and \( d_2 \)).
- Perimeter (P): \( P = 2 \times (a + b) \)
- The perimeter is twice the sum of the lengths of the two distinct pairs of adjacent sides (\( a \) and \( b \)).

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8. Circle

- Area (A): \( A = \pi r^2 \)
- The area is calculated using the radius (\( r \)) and the constant \( \pi \).
- Circumference (C): \( C = \pi d = 2 \pi r \)
- The circumference is the distance around the circle, calculated using either the diameter (\( d \)) or the radius (\( r \)).

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9. Annulus

- Area (A): \( A = \pi (R^2 - r^2) \)
- The area of an annulus (the region between two concentric circles) is the difference in the areas of the larger circle (radius \( R \)) and the smaller circle (radius \( r \)).

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Summary of Formulas:

| Shape | Area (A) | Perimeter/Circumference (P/C) |
|----------------|-----------------------------------|---------------------------------------|
| Rectangle | \( l \times w \) | \( 2 \times (l + w) \) |
| Square | \( s^2 \) | \( 4 \times s \) |
| Triangle | \( \frac{b \times h}{2} \) | \( s_1 + s_2 + s_3 \) |
| Parallelogram | \( b \times h \) | \( 2 \times (l + w) \) |
| Trapezium | \( \frac{(a + b) \times h}{2} \) | \( a + b + c + d \) |
| Rhombus | \( \frac{d_1 \times d_2}{2} \) | \( 4 \times s \) |
| Kite | \( \frac{d_1 \times d_2}{2} \) | \( 2 \times (a + b) \) |
| Circle | \( \pi r^2 \) | \( \pi d = 2 \pi r \) |
| Annulus | \( \pi (R^2 - r^2) \) | Not applicable |

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These formulas are essential for solving problems involving the measurement of areas and perimeters of different geometric shapes. If you have a specific problem to solve, feel free to provide the details, and I can help you apply these formulas!

Final Answer:
\[
\boxed{\text{See detailed explanations above}}
\]