In order to find an area or a perimeter, it is not necessary to have great knowledge of geometry.
There are ways to do this without calculations, but methods that require knowledge of formulas and the ability to use them are most accurate.
If you have a shape of an arbitrary area, forWhich you need to determine the area and perimeter, and you can not use the usual formulas for calculations, since this is not a rectangle, circle or trapezoid, and something is more difficult to configure, first of all, divide this shape into parts. Typically, polygons are divided into triangles, if your given shape has curved lines in the perimeter, select triangles and segments of the circle. Complete the segments to the full circle in order to be able to measure the desired values.
Dividing all the figures into similar elements,Count for each of them an area. The area of the triangle is equal to half the length of one of its sides to the height, lowered to this side. Measure the ruler for each triangle with the desired lengths, substitute the values in the formula and calculate the area of each triangle. If you selected except for triangles, as elements, and segments of a circle, consider their area according to the formula? 2 * a / 360-S, where a? This is the central angle, two radii of which are interconnected by an arc of the segment-S? The area of the triangle formed by the same radii and straight line, which can be arched by connecting radii.
When you know all the areas of individual elements, summarize them to find out the area of the desired figure.
To find out the perimeter, you need to measure allRectilinear segments in it and fold them. Then add the calculated lengths of the arcs to the resulting number. The length of the arc of the circle is calculated as the product of the radius of the circle by the angle a, already mentioned above.
You can limit yourself to the minimum of calculations, ifUse other methods to determine the area. So you can use the pallet. Put a pallet on top of the figure for which you define the area, recalculate all units of area overlapping the required area, and then multiply the resulting number by the known area of the measuring unit of the pallet.
Requires more weighting toolsArea determination. If you have an accurate scale, copy the image of the desired area to a sheet of a known format, weigh it. Now cut out the image of the figure and measure its weight. When you know the area and weight of the whole sheet, as well as the weight of its part, you can make a proportion and determine the area of this part. It is better to use this method if the paper is factory-made.
And the easiest way to measure the perimeter,Lay a thread along the entire perimeter line. It is important that the thread exactly matches the perimeter. When the thread closes, that is, makes a full circle along the perimeter line, mark the point on it, in which the thread has touched the origin point. Cut and measure the length obtained, the value of your measurement - this is the perimeter of this figure.