![]() ![]() Is to tessellate it with a fundamental region, often using a grid,Ĭount the number of such regions used, (in whole or in part), Refrain (and not by singing a sad song) from utilizing this shortcut.Ī common way to measure area, or the space covered by a region, However, students have a tendancy to mix the feet (') and inch (")ĭesignations with the metric notation and I take a VERY dim view of Or the metric notation m 2 or some combination thereof. These are often specified using the English notation: square feet (sq. General Area Area is the two-dimensional measurement of the interior of a polygonĪs we transition into area we will be using square units extensively. Thus the perimeter is 16" even though the figure might not otherwise be We can note that all the horizontal top sides sum to 5" as do the bottom,Īnd all the vertical left sides sum to 3" as do the right. Suppose you know the overall length and width to be 5 in. On this topic I note here againĪ common puzzle for finding area is show at the right. Which in my experience is problematic for students going on to precalculusĪnd calculus (all our students) where angle measurements without units areĪssumed to be in radians. Units so often the generic term units will be used.Īs mentioned previously, the textbook also omits the degree symbol (°) Our textbook is not very good about specifying Provided many useful conversions, especially noting useful ones between The world and science uses MKS or SI (metric) whereas most American citizensĬommonly think in English units. We will start earnestly deducting points if units are omitted (or wrong). & Tech., Spring 2003, page 11) not only the weather, was an importantįactor in the English defeat of the Spanish Armada in 1588. In fact, recent discoveries have lead to the conclusion that See these write ups about the 1/8 billion dollar Wrong assumptions about units can be very costly. Specifying units is very important in science. While we are on the topic of units, now is a good time to stress some Them will be very helpful in solving problems. ![]() You will generally get away with this in geometry,īut in chemistry and physics specifying units and properly converting between Note the casual dropping of units during calculation, but specification of What is, for example, the perimeter of a rectangle with width 0.01 unitsĪnswer: Since A = lw (see below) and A = 100 andĭividing both sides by 0.01 (and applying symmetry) gives l = 10000. ![]() If its length is virtually infinite and its width is infintesimal. (each side of 10 units) to virtually infinite, In fact, rectangles with an area of 100 units 2Ĭan vary in perimeter from as small as 40 units Irregularly shaped regions can have very large perimeters relative to their area. If not, solving such problems is one of the reasons calculus was invented! Hopefully, this will be a good enough approximation. Object, say, a kidney shaped swimming pool.Īnswer: Possibly lay a rope along the perimeter and then measure Recall that we also used the word parameter in conjuctionĬonsider how you might measure the perimeter of an irregularlly shaped Thus we see perimeter can be one parameter describing a circle, hence much Of whose values characterize a member of a system. The word parameter is so often interchanged with perimeter that we Often the sides of a rectangle are referred to as its length and width. Say x and y, the perimeter is equal to 2 x + 2 y. In fact, for any regular n-gon with sides of length sįor rectangles or kites which have only two different side lengths, Thus for squares with four equal sides of length s, ![]() The more sides there are of equal length, the simpler the formula. Straight-forward as to be rather trivial. It is one way to measure the size of something.įormulae abound, but for triangles and quadrilaterals they are so Perimeter is a one-dimensional measurement.
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