Area Calculator

How to Calculate Area

Calculating the area of different shapes is a fundamental skill in geometry. Here's a comprehensive guide on how to calculate the area for various shapes:

Area Formulas

• Rectangle: \(A = l \times w\)
• Square: \(A = s^2\)
• Triangle: \(A = \frac{1}{2} \times b \times h\)
• Circle: \(A = \pi r^2\)
• Ellipse: \(A = \pi ab\)
• Sector: \(A = \frac{1}{2} r^2 \theta\) (where \(\theta\) is in radians)
• Segment: \(A = r^2 \arccos\left(1 - \frac{h}{r}\right) - (r - h)\sqrt{2rh - h^2}\)
• Annulus: \(A = \pi (R^2 - r^2)\)
• Trapezoid: \(A = \frac{1}{2}(b_1 + b_2)h\)
• Parallelogram: \(A = bh\)
• Rhombus: \(A = \frac{1}{2}d_1d_2\)
• Kite: \(A = \frac{1}{2}d_1d_2\)
• Regular Polygon: \(A = \frac{1}{4}ns^2\cot(\frac{\pi}{n})\)
• Irregular Quadrilateral: \(A = \frac{1}{2}d_1d_2\sin\theta\)
• Rectangular Border: \(A = lw - (l - 2t)(w - 2t)\)

Calculation Steps

1. Identify the shape and its relevant measurements.
2. Choose the appropriate formula for the shape.
3. Substitute the measurements into the formula.
4. Perform the calculations to obtain the area.
5. Round the result to the desired number of decimal places, if necessary.

Example Calculation

Let's calculate the area of a rectangle with length 5 units and width 3 units:

1. Shape: Rectangle
2. Formula: \(A = l \times w\)
3. Substituting values: \(A = 5 \times 3\)
4. Calculating: \(A = 15\) square units

Visual Representation

This visual representation shows a 5x3 rectangle with its dimensions and total area of 15 square units. The grid pattern helps visualize the square units that make up the total area.