![]() The Area Addition Postulate says that if we have two shapes that do not overlap, the total area equals the sum of the areas of the individual shapes. All it takes is a little common sense in the form of a neat little postulate. We threw circles in there for good measure, but what about the billions of other polygons that we haven't talked about? Do they have individual area formulas too? Probably, but instead of memorizing them all, we can simplify our lives a great deal. So far, we've only looked at the areas of triangles and various quadrilaterals. The problem asks for area, so we can plug this into the area formula for a circle. The radius must be the distance between these two points. We're given two points: one is the center and the other is a point on the circle. We know that the area of a circle is A = π r 2, so that's an excellent start. Sample ProblemĪ circle with center (-2, 2) has a radius that extends to (1, 0). Some require us to use the distance formula. Unfortunately, not all shapes take such a comfortable position on the coordinate plane. Since the trapezoid is aligned to the grid, we don't even have to use the distance formula. The two parallel sides, AD and BC, are the bases and luckily, we know that AB is the height. Now we know to use the formula A = ½( b 1 + b 2) h. (If you don't believe that, make sure the slopes of AD and BC are equal and that AB has a slope that's the negative reciprocal.) It's fairly obvious now that we have a right trapezoid. ![]() After all, do we have a rectangle? A kite? A parallelogram? Actually plotting the points might give us a better sense of which formula to use. What is the area of the quadrilateral?Īt first glance, it might be tough to tell exactly which formula to use. Sample ProblemĪ quadrilateral has four vertices at A (-1, 4), B (-1, 0), C (6, 0), and D (3, 4). To be sure of which formula we need to use, it's best to actually draw everything out so we can be certain that the shapes are what we think they are (for instance, a rhombus and not a kite). However, unlike finding perimeters and side lengths, area is different because the formulas for area differ based on the shapes we have. In other words, we'll need our trusty distance formula to help us find bases, heights, diagonals, and radii. If 2D shapes can live on the x-y plane, we can use the nature of the Cartesian coordinate system to help us find the areas of these figures. Where better for 2D shapes to find themselves than on the x-y coordinate plane? There's plenty of legroom for as many shapes as we need, and plotted points will help these shapes find themselves. For others, it's more symbolic, like the open road or their hobbies. For some, it's a physical place like a room or a mountaintop. A place we can go when we need to get in touch with ourselves again. We all need a shelter, a safe haven when things get rough. Coordinates and the Area Addition Postulate
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