Mensuration and trigonometry Study Guide

The area of a circle represents the entire two-dimensional space enclosed within its boundary. Think of it as the amount of paint you would need to cover the face of a circular object like a coin or a frisbee. To calculate this area, you need to know the circle's radius. The radius is the distance from the very centre of the circle to any point on its edge. The formula used for calculating the area of a circle is A = πr², where 'A' stands for the area, 'r' stands for the radius, and π (pi) is a special mathematical constant, approximately equal to 3.14159. This formula means you multiply pi by the radius squared (radius multiplied by itself).

If you are given the diameter instead of the radius, remember that the diameter is twice the length of the radius (d = 2r). So, to find the radius from the diameter, you simply divide the diameter by 2 (r = d/2). Once you have the radius, you can then apply the area formula. For example, if a circle has a diameter of 10 cm, its radius would be 10 cm / 2 = 5 cm. Then, the area would be A = π × (5 cm)² = 25π cm². Depending on the question, you might leave the answer in terms of π or calculate a numerical value using an approximation for π, often 3.14 or the calculator's π button, rounding to a specified number of decimal places or significant figures.

A composite shape is any shape made up of two or more basic geometric shapes, such as rectangles, squares, triangles, or circles. To find the area of a composite shape, you need to break it down into these simpler, familiar shapes. The general method involves identifying the basic shapes that form the composite figure, calculating the area of each individual basic shape using the appropriate formula, and then adding these individual areas together to find the total area of the composite shape. Sometimes, a composite shape might resemble a larger basic shape with a smaller basic shape 'removed' or 'cut out' from it. In such cases, you calculate the area of the larger shape and then subtract the area of the smaller shape. For example, an L-shaped room can be seen as two rectangles joined together, or as a larger rectangle with a smaller rectangular 'bite' taken out of one corner. Carefully identifying the component shapes and applying the correct area formulas (e.g., length × width for a rectangle, 0.5 × base × height for a triangle) are key steps to accurately calculating the area of any composite figure. Always pay attention to given dimensions and ensure you use consistent units throughout your calculations.