#3A6ED6

#DA2570

#C75000

$\textsf{SA =}$

$\bold\textsf{Fold / Unfold}$

#4D4D4D

$\text{Check}$

$\text{NEUES PRISMA}$

No selection allowed for all input boxes

Fix position and allow selection for all text objects

Empty all input boxes

Reset app

\text{Simplify your answer.}

#006758

#B00020

#252525

#757575

#949494

#E44461

#DA2570

#E66B9E

#3A6ED6

#5991FF

#008475

#0F8538

#00a83c

#5145A8

#6557D2

#8575FF

#903D14

#BD6C43

#E07415

#eeeeee

#2E006758

#2EB00020

\textsf{\bold{\pi} units^2}

view

\text{Netz öffnen}

$\textsf{VARIABLEN ERSETZEN}$

\textsf{Erkunde den Oberflächeninhalt regelmäßiger\Prismen.}

\textsf{Die Höhe des Dreiecks ist auf eine\Nachkommastelle gerundet.}

countQuestion = 0
allRandomSeeds = RandomUniform(0, 0.99, 200)
numRandoms = 4
randIndex: (Mod[countQuestion, floor(Length[allRandomSeeds] / numRandoms)] * numRandoms) + 1
currentRandomSeeds = Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1)
randomSideLength = If(countQuestion ≟ 0, 4, floor((currentRandomSeeds(2) * 5)) + 1)
l1 = KeepIf(Mod[randomSideLength, kk] ≟ 0, kk, Sequence[randomSideLength])
heiFact = If(countQuestion ≟ 0, 1, Element[l1, floor((currentRandomSeeds(4) * Length[l1])) + 1])
hei_{1} = If(countQuestion ≟ 0, 2, (floor((currentRandomSeeds(1) * 4)) + 1) / heiFact)
Case = If(currentRandomSeeds(3) ≤ 0.5 ∨ countQuestion ≟ 0, 4, 3)
ymin: (-hei_{1}) - If[Case ≟ 4, 1, 0]
ymax = If(Case ≟ 4, hei_{1} + 3, (hei_{1} * sin(30°)) + 1.5)
randomHeight_{1}: (hei_{1} * randomSideLength)
hei2: randomHeight_{1}
tCil2 = 0 (slider from 0 to 1, step 0.01)
poly1 = Polygon((0, 0), (1, 0), 3)
B = Centroid(poly1)
baseTri = Translate(poly1, Vector[B, (0, 1)])
prism3, G, H, I, face5, face7, face6, faceGHI, edge7, edge9, edge10, edgeGH, edgeHI, edgeGI = Prism(baseTri, hei_{1})
c, J, K, L, M, N, O, P, Q, R, S, faceJKL, faceJKNM, faceKLPO, faceJLQR, faceMNS, edgeJK, edgeKL, edgeJL, edgeJM, edgeMN, edgeKN, edgeKO, edgeOP, edgeLP, edgeLQ, edgeQR, edgeJR, edgeNS, edgeMS = Net(prism3, tCil2)
LabelTriPos = Midpoint(edgeJK)
triHeight = Segment(L, LabelTriPos)
triHeightNum: round((Length[triHeight] * randomSideLength), 1)
expAns: ((Case * randomSideLength) * hei2) + ((2 * randomSideLength) * If[Case ≟ 3, triHeightNum / 2, randomSideLength])
countQuestion_{1}: countQuestion
wait = 1 (slider from 0 to 1)
showhint = false
input1 = NaN
InputBox1 = Textfield(input1)
correct2: ¬Defined[IndexOf["+", Text[InputBox1 + "", false]]]
correct1: abs(input1 - expAns) ≤ 0.01
BaseCenter_{1}: (0, 1, 0)
tCil_{1}: (-tCil2)
θCil_{1}: (pi * (1 - abs(tCil_{1})))
rCil_{1}: pi / θCil_{1}
input2: NaN
validate = false
showanswer = false
showsolution = false
tries = 0
countCorrect = 0
correct: correct1 ∧ correct2
showbuttons = true
typicalError1: 0
typicalError2: 0
showhinttypicalerror = false
labelBtnValidate: "\text{CHECK (" + (LaTeX[3 - tries]) + ")}"
ϕCil_{1}: (abs(tCil_{1}) * pi / 2)
CC_{1}: (0, 0, hei_{1})
speed_{1} = 3
TV_{1}: (2, -2, 2)
segRad_{1} = Segment((0, 1, 0), (1, 1, 0))
labelRadius_{1}: "\textsf{" + (LaTeX[randomSideLength]) + "}"
E_{1}: (0, 4, 0)
F_{1}: (0, 2.3, 0)
G_{1} = (-4, 2, 0)
H_{1} = (-3.3583487139075943, -0.4495427412317252, 0)
J_{1} = (2.404933095475027, 5.737861179470774)
MoveGuideLines_{1} = (2.1206684278417285, 3.5771759730725914)
verticalGuideLine_{1}: x = x(MoveGuideLines_{1})
AppSize: (x(Corner[1, 5]) + x(CornerThreeD[-1, 9]), y(Corner[5]))
TopPoint = Rotate((0, 0, hei_{1}), (pi / 2 * tCil_{1}), Line[(1, 0, 0), (-1, 0, 0)])
u = Vector((0, cos((tCil_{1} * pi)), (-sin((tCil_{1} * pi)))))
v = Vector((0, sin((tCil_{1} * pi)), cos((tCil_{1} * pi))))
f: y = y(MoveGuideLines_{1})
App2DSize = Corner(5)
textCountCorrect: "\text{Number correct: " + (LaTeX[countCorrect]) + " }"
normView = (0.8572814316582401, -0.4751988572105508, -0.19812771900919046)
isTypicalError: ¬correct2
xFeedback: 16 + If[correct ∨ tries ≟ 3, -5, 149]
yfeedback: 213 + If[correct, 6, 1]
labelHeight_{1}: "\textsf{" + (LaTeX[If[hei2 ≤ 9, "\phantom{0}", ""]]) + "" + (LaTeX[hei2]) + "}"
textFeedback: "" + (LaTeX[If[correct, "$\text{✓ Correct}$", "$\text{✕ " + (If[tries < 3, "Try again", "Maybe next time"]) + "}$"]]) + ""
inputSaved: {NaN}
inputCurrent: {input1, If[correct2, 1, 0]}
enableBtnValidate: inputCurrent ≠ inputSaved ∧ inputCurrent ≟ RemoveUndefined[inputCurrent]
enableInput: tries < 3 ∧ (¬(validate ∧ correct))
layoutX: 16
layoutY: 210
f' = Translate(f, Vector[(Vector[Corner[4], Corner[1]] / 500 * 16)])
stage = 0
textSolution: "\textsf{O}= " + (LaTeX[Case]) + " \times \bold\textcolor{" + (LaTeX[colorBlue_{1}]) + "}{" + (LaTeX[randomSideLength]) + "} \times \bold\textcolor{" + (LaTeX[colorPink_{1}]) + "}{" + (LaTeX[hei2]) + "} + 2 \times" + (LaTeX[If[Case ≟ 3, "\frac{1}{2}\times", ""]]) + " \bold\textcolor{" + (LaTeX[colorBlue_{1}]) + "}{" + (LaTeX[randomSideLength]) + "}" + (LaTeX[If[Case ≟ 4, (("\bold\textcolor{" * colorBlue) * "}{^{2}}"), (((("\times\bold\textcolor{" * colorOrange) * "}{") * triHeightNum) * "}")]]) + " \\\textsf{O}=" + (LaTeX[expAns]) + "\text{ Einheiten²}"
showcyl: wait ≟ 1
speedWait: 20
baseSqare = Polygon({(-0.5, 1, 0), (0.5, 1, 0), (0.5, 0, 0), (-0.5, 0, 0)})
prism4, C, D, E, F, face1, face3, face4, face2, faceCDEF, edge1, edge2, edge3, edge4, edgeCD, edgeDE, edgeEF, edgeCF = Prism(baseSqare, (-hei_{1}))
a, W, Z, A_1, B_1, C_1, D_1, I_1, K_1, M_1, N_1, O_1, P_1, Q_1, R_1, face8, face9, face11, face12, face10, face13, edgeWZ, edge11, edge14, edge5, edge6, edge19, edge12, edge13, edge22, edge15, edge16, edge23, edge17, edge18, edge24, edge8, edge21, edge25, edge20 = Net(prism4, tCil2)
App3DSize = CornerThreeD(-1, 9)
DirViewIni = (-0.4698463103929541, 0.8137976813493736, -0.3420201433256689)
LabelHPos = Midpoint(edge15)
LabelSqPos = Midpoint(edge5)
view = Vector((1; (pi / 2 * tCil2) + (pi / 6 * (1 - tCil2)); ((-pi)) / 2 + ((0.8 * pi / 2) * (1 - tCil2))))
A = CornerThreeD(-1, 13)
xmax: (ymax - ymin) / 2
LabelHPos3 = Midpoint(edgeKO)
text5 = Text(hei2, If[Case ≟ 3, LabelHPos3, LabelHPos], true, true)
text7: "" + (LaTeX[labelRadius_{1}]) + ""
widLabelSide = Distance(Corner[text7, 2], Corner[text7, 1])
text4 = Text(randomSideLength, LabelTriPos - ((tCil2 * widLabelSide / 2), 0), true, true)
heiLabelSide = Distance(Corner[text7, 4], Corner[text7, 1])
L' = Translate(L, Vector[(x(O) + 0.1, 0, 0)])
LabelTriPos' = Translate(LabelTriPos, Vector[(x(O) + 0.1, 0, 0)])
triHeight' = Segment(L', LabelTriPos')
text8 = Text(triHeightNum, Midpoint[triHeight'] + (If[x(O) ≥ 3, -1, 0], heiLabelSide / 2), true, true)
questiontext_{1}: "\textsf{Formel für den Oberflächeninhalt (O):}\\\\
\textsf{O = \color{" + (LaTeX[colorPink_{1}]) + "}Mantelfläche \color{}}+ 2 \times \color{" + (LaTeX[colorBlue_{1}]) + "}\textsf{Grundfläche}\\
\textsf{O = }" + (LaTeX[Case]) + "\times\textcolor{" + (LaTeX[If[stage ≟ 1, colorPink_{1}, colorBlack]]) + "}{" + (LaTeX[If[stage ≟ 2, (("\bold\textcolor{" * colorBlue_{1}) * "}")]]) + "a \times " + (LaTeX[If[stage ≟ 2, (("\bold\textcolor{" * colorPink_{1}) * "}")]]) + "h }+ 2 \times \textcolor{" + (LaTeX[If[stage ≟ 1, colorBlue_{1}, colorBlack]]) + "}{" + (LaTeX[If[Case ≟ 3, "\frac{1}{2} \times ", ""]]) + "" + (LaTeX[If[stage ≟ 2, (("\bold\textcolor{" * colorBlue_{1}) * "}")]]) + "a" + (LaTeX[If[Case ≟ 3, (("\times" * If[stage ≟ 2, (("\bold\textcolor{" * colorOrange) * "}"), ""]) * "{h_G}"), ((("\bold\textcolor{" * colorBlue) * "}") * "^{2}")]]) + "}\\" + (LaTeX[If[stage ≟ 2, textSolution, ""]]) + ""
text6 = Text(randomSideLength, LabelSqPos + (0, 0.25, (0.25 * tCil2)), true, true)
zmin: ((ymin - 1) * 5 / 4)
zmax: (((-ymin) + 1) * 5 / 4)
CentView: (0, (ymin + ymax) / 2, (zmin + zmax) / 2)
xmin: (-xmax)
w = Vector(Midpoint[triHeight'], Vertex[triHeight', 1])
b = Vector(Midpoint[triHeight'], Vertex[triHeight', 2])
tabOrder: {text3, text2, tCil2, questiontext_{1}, btnReplaceVariables, btnNew}