My surname is Marilynn This is a high school question. Ns never had th chance to learn even simple algerbra in school. I have been trying to learn. I understand a circumfrance, diameter, and radius. I have learned what pie is and also why the is dubbed pie and that that is about 3.14. My child is irritable that i can"t help him v his math, The problem is this: A one is evenly separated into six equal triangle leaving one area between the exterior of the circle and also the one side of the triangle. This area is measured as 3.14. Ns think they supplied the number 3.14 to try to throw me off, knowing that pie equalls 3.14. What is the size of the radius, one line on the triangle? ns wish I might draw girlfriend a picture. I hope i am clean in what ns mean. The would median so lot to me if you could aid me and it explaine it to me as merely as possible for mine brain. Thank you so really much. Sincerely, Marilynn

hello Marilynn, First, I will certainly tell you mine assumptions around what your snapshot looks like: every triangle has actually a peak (corner) at the centre of the one each triangle has corners ~ above the circumference of the one (so, 2 sides of every triangle is a radius) The triangles share sides (there room no gapes in between triangles) The overall picture looks favor a flower - each triangle is a petal. The unknown area is what is left around the exterior of the circle, between the circumference and the outside side of each triangle. This unknown area is split into 6 congruent sections (equal in every method - choose the triangles space "equal" in every way - consisting of area, size of side and length of arc). It is not clear whether you typical the area of one arc is Pi (not actually split Pie, back pronouced the same), or all 6 sections taken with each other is Pi. In what follows, I will assume that among the external sections has an area the Pi, so the the area of all 6 sections taken with each other is 6 times Pi. We require to uncover the radius the the circle, call it r.

i will also use ns to was standing for Pi (or approx. 3.14). Now, there is a many of info we deserve to garnish from the triangles: The angles at the center are all 60 degrees. This is due to the fact that the 6 angles in ~ the center are every equal, and also a circle has 360 degrees. So execute 360 edivided by 6. each triangle is Isosceles. This is because two sides space equal (the political parties that space a radius). every triangle, is in reality equilateral. Because it is iscoceles, the two external angles are also equal. But there is 180 degrees in a triangle, 60 are currently used in the center angle, leaving 180-60=120 degrees for the external angles. But, 120 divided by 2 is 60 degrees, for this reason all three angles are equal, so that is isoscles. Every side in every triangle is of length r. This is since we have 6 congruent ("equal" in every way) equilateral triangles, and also because 2 sides the every triangle is a radius. native the geometry the the triangles, we should do some algebra. Due to the fact that we understand an area, and we require a radius, we require a formula (or equation) because that radius in regards to area (in what follows, keep the score of a formula in mind). The area of the one is P*r2 (r2 way r squared, and also * means multiply) The area of the leftover sections external the triangles, however inside the one (an area we currently no to it is in 6*P), can additionally be discovered by individually the area the the triangle from the area of the circle. We need to uncover an area of among the it is provided triangles. technique 1 for calculating an area the a triangle The area of a triangle is b*h/2 This is whereby some trigonometry is needed: draw a line from a vertex to an opposite side the divides the opposite side in half and is at right angles. This divides the it is provided triangle into two congruent best angled triangles, and also the brand-new side is the height, call it h. We need to uncover h. utilizing trig in among the appropriate angled triangles, we have actually sin60 = h/r yet sin60 = sqr(3)/2, whereby sqr(3) means the square root of 3 so sqr(3)/2 = h/r main point both political parties by r to obtain h = r*sqr(3)/2 r Now, the area the one it is intended triangle is b*h/2 = (r)*(r*sqr(3)/2)/2 = (r2)*sqr(3)/4 technique 2 because that calculating an area of a triangle Heron"s formula for the area the a triangle is: sqr(s*(s-a)*(s-b)*(s-c)), wherein a,b,c space the sides and also s is half the perimeter due to the fact that each next is the radius, the perimeter is 3*r, so half the perimeter is 3*r/2 Now, the area that one equalateral triangle is: sqr((3*r/2)*(3*r/2 - r)*(3*r/2 - r)*(3*r/2 - r)) = sqr((3*r/2)*(r/2)*(r/2)*(r/2)) =sqr(3*(r4)/16) =(r2)*sqr(3)/4 notice that we obtain the very same answer as method 1 - I had this in case you didn"t know any type of trigonometry. Recall that the area of the one minus the area of all 6 triangles is the area the the leftover sections. From this we can now create an equation: P*r2 - 6*(r2)*sqr(3)/4 = 6*P part algebra is necessary to solve for r: factor r2 on the left side (r2)*(P-6*sqr(3)/4) = 6*P obtain r2 be chin by dividing: r2 = 6*P/(P-6*sqr(3)/4) take it the square root of both sides: r = sqr(6*P/(P-6*sqr(3)/4)) use order of operations to calculation on a calculator (with P=3.14): r= 5.896... So, the radius that the one is approx.


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