["square", "circle", "triangle"]
randFromArray(SHAPES)
randFromArray(SHAPES)
randRange(2, 6)
randRange(INNER_SIZE + 1, 11)
{square:function(e,r,s){var n=2*s,t=[[e-s,r+s],[e+s,r+s],[e+s,r-s],[e-s,r-s],!0];return{name:$._("cuadrado"),vertices:_.initial(t),contains:function(n){return n[0]>=e-s&&n[0]<=e+s&&n[1]>=r-s&&n[1]<=r+s},drawShape:function(e,r){return e.path(t,r)},drawSize:function(t,a,i){return{label:i?t.label([e,r+s],n,"above",a):t.label([e+s,r],n,"right",a),path:i?t.path([[e-s,r+s],[e+s,r+s]],a):t.path([[e+s,r+s],[e+s,r-s]],a)}},hint:function(){return"\\text{"+$._("área de un cuadrado")+"} = s^2 = "+n+"^2"}}},circle:function(e,r,s){return{name:$._("círculo"),vertices:_.map([0,30,45,60,90,120,135,150,180,210,225,240,270,300,315,330,360],function(e){return e=e*Math.PI/180,[s*Math.cos(e),s*Math.sin(e)]}),contains:function(n){return pow(n[0]-e,2)+pow(n[1]-r,2)<=s*s},drawShape:function(n,t){return n.circle([e,r],s,t)},drawSize:function(n,t,a){return{label:n.label(a?[e-s/2,r]:[e+s/2,r],s,"above",t),path:n.path([[e,r],a?[e-s,r]:[e+s,r]],s,t)}},hint:function(){return"\\text{"+$._("área de un círculo")+"} = \\pi r^2 = \\pi "+s+"^2"}}},triangle:function(e,r,s){var n=2*s,t=[[e,r],[e+n,r],[e+n/2,r+sqrt(3)*n/2]],a=[(t[0][0]+t[1][0]+t[2][0])/3,(t[0][1]+t[1][1]+t[2][1])/3];t=_.map(t,function(e){return[e[0]-a[0],e[1]-a[1]]}),t.push(!0);var i=function(e,r,s){return(e[0]-s[0])*(r[1]-s[1])-(r[0]-s[0])*(e[1]-s[1])};return{name:$._("triángulo equilátero"),vertices:_.initial(t),contains:function(e){var r,s,n;return r=i(e,t[0],t[1])<=0,s=i(e,t[1],t[2])<=0,n=i(e,t[3],t[0])<=0,r==s&&s==n},drawShape:function(e,r){return e.path(t,r)},drawSize:function(e,r){return{label:e.label([(t[0][0]+t[1][0])/2,(t[0][1]+t[1][1])/2],n,"below",r),path:e.path([t[0],t[1]],n,r)}},hint:function(){return"\\text{"+$._("área de un triángulo equilátero")+"} = \\dfrac{\\sqrt{3}}{4}s^2 = \\dfrac{\\sqrt{3}}{4}"+n+"^2"}}}}
DRAW[OUTER_SHAPE](0, 0, OUTER_SIZE)
DRAW[INNER_SHAPE](0, 0, INNER_SIZE)
{square:function(e){return[Math.pow(2*e,2),Math.pow(2*e,2)]},circle:function(e){return[Math.PI*e*e,piFraction(Math.PI*e*e)]},triangle:function(e){return[e*e*Math.sqrt(3),e*e+"\\sqrt{3}"]}}
AREAS[OUTER_SHAPE](OUTER_SIZE)
AREAS[INNER_SHAPE](INNER_SIZE)
OUTER_AREA - INNER_AREA
$._("\u00e1rea de la figura completa")
$._("\u00e1rea de la regi\u00f3n interior")
$._("\u00e1rea de la regi\u00f3n sombreada")
El INNER.name está dentro del OUTER.name en el diagrama.
¿Cuál es el área de la región sombreada?
SHADED_AREA
var g=init({range:[[-14,14],[-14,14]],scale:[11,11]});graph.outerShape=OUTER.drawShape(g,{fill:BLUE,stroke:BLUE,"fill-opacity":.5}),graph.innerShape=INNER.drawShape(g,{fill:"#f8f8f8",stroke:BLUE}),graph.outerSize=OUTER.drawSize(g,{stroke:BLUE,opacity:1}),graph.innerSize=INNER.drawSize(g,{stroke:ORANGE,opacity:1},!0)
Primero calcula el área de la figura completa (incluyendo el área sin sombrear), junto con el área de la región interior sin sombrear.
OUTER.drawShape(KhanUtil.currentGraph,{fill:BLUE,opacity:.5})
\text{AREA_OF_WHOLE_FIGURE} =
\qquadOUTER.hint() = PRETTY_OUTER_AREA
\text{AREA_OF_INNER_REGION} =
\qquadINNER.hint() = PRETTY_INNER_AREA
Luego, resta el área de la región interior del área de la figura completa, para encontrar el área de la región sombreada (la diferencia entre las dos áreas).
\text{AREA_OF_SHADED_REGION} = PRETTY_OUTER_AREA - PRETTY_INNER_AREA = roundTo(2, SHADED_AREA)