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Just call them 5 triangles like this minus their basis, right, if i take the perimeter of all of these sides If i added up the part that should not be part of the perimeter of the star would be this part,that part, that part,that part, that part and that part.those are not the part, those are not the part of the perimeter of the star so should be the perimeter of the 5 triangles minus the links of their bases links of their 5 bases. well, the perimeter of each of them is 30, perimeter of 5 of them is going to be 5 times 30 which is 150, now we want to subtract out the links of their 5 bases now the links of their 5 bases if we add them up is the exact perimeter of this in inner pentagon right over here.So it is this side, let me do this in a new color actually So the perimeter of the triangle i will do in orange.
And the most obvious thing to do here is started A and just drop a rock drop an altitude right over here, and so this line right over here is going to hit at 90 degrees and we could call this point E.
And what is interesting here is we can split this up into something we recognize a rectangle and a right triangle.
They then tell us that the perimeter of FGHIJ So FGHIJ the perimeter of this pentagon right over here is 50 So if I add up that side plus that side plus that side plus that side, plus that side, I get 50.
And then they say what is the perimeter of the star?
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The base is d, and the perpendicular distance is the same as the y value for the point (4,6). Now, we'll need the formula for a triangle's area: A = (1/2) base * height A = 1/2 * 6.71 * 6 A ≅ 20.1 If the units are feet, then Fred has 20.1 square feet of garden to surround with 35.1 feet of fencing.
Fred is amazed how all of this information comes from 3 coordinates! When the vertices are given as coordinates, or the point's location in the xy-plane, we can find the perimeter and area.