Final answer:
To calculate the area of a bounded region, one must add up the areas of the individual shapes that compose the region, such as rectangles and triangles, considering the correct units and significant figures for accuracy.
Step-by-step explanation:
When attempting to find the area of a bounded region, it is essential to calculate the individual areas of simple geometric shapes that compose the region. For instance, if we are given a graph with a shaded area that includes a rectangle and a triangle, we need to calculate the area of each shape. The area of a rectangle is found by multiplying its length by its width, while the area of a triangle is ½ the base times the height.
It's also important to consider the units used and to ensure final answers are presented with the correct number of significant figures. If we are using meters, and the conversion to square meters is necessary, one must remember to handle units properly, ensuring the answer contains appropriate significant figures.
In situations where we need a rough estimate of the area under a curve, one can draw a rectangle over an estimated average height of the curve and calculate its area. This gives a crude approximation when precise calculations are not required, such as estimating the area of a regulation basketball court. However, for more precise calculations, one should use calculus to find the exact area under the curve.