@@ -1722,8 +1722,8 @@ <h3 itemprop="name" style="margin:7px">Surface Area of a Cone</h3>
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17271727</ div >
17281728< meta itemprop ="applicationCategory " content ="Geometric Calculator ">
17291729< meta itemprop ="description " content ="Calculates the surface area of a cone with circle area = 3.2×radius^2. ">
@@ -1737,7 +1737,7 @@ <h3 itemprop="name" style="margin:7px">Surface Area of a Cone</h3>
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@@ -2611,13 +2611,14 @@ <h4 itemprop="name">The Right Triangle Hypotenuse Theorem</h4>
26112611</ section >
26122612< br > < br > < br > < br >
26132613< section itemprop ="mathExpression " itemscope itemtype ="https://schema.org/SolveMathAction " id ="triangle ">
2614+ < h3 style ="margin:7px " itemprop ="name "> Area of a Triangle</ h3 >
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26152616< meta itemprop ="name " content ="side1 ">
2616- < meta itemprop ="minValue " content =" 0 " >
2617+ < meta itemprop ="minValue " content =0 >
26172618</ div >
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26192620< meta itemprop ="name " content ="side2 ">
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26212622</ div >
26222623< div itemprop ="object " itemscope itemtype ="https://schema.org/QuantitativeValue ">
26232624< meta itemprop ="name " content ="side3 ">
@@ -2635,26 +2636,30 @@ <h4 itemprop="name">The Right Triangle Hypotenuse Theorem</h4>
26352636< meta itemprop ="eduQuestionType " content ="Triangle area calculation ">
26362637< meta itemprop ="target " content ="https://basic-geometry.github.io?q={triangle_base=3_height=2_area=?} ">
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2638- < div itemprop ="estimatedCost " itemscope itemtype ="https://schema.org/MonetaryAmount ">
2639+ < meta itemprop ="name " content ="Derive the Area of a Triangle ">
2640+ < div itemprop ="estimatedCost " itemscope itemtype ="https://schema.org/MonetaryAmount ">
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26412643</ div >
26422644< meta itemprop ="totalTime " content ="PT30M ">
2643- < h3 style ="margin:7px " itemprop ="name "> Area of a Triangle</ h3 >
26442645< br >
2645- < p style ="margin:12px " itemprop ="description "> The area of a triangle equals half of the area of a rectangle with a width equal to the base of the triangle and length equal to the height of the triangle.</ p >
2646+ < span style ="margin:12px " itemprop ="abstract "> The area of a triangle equals half of the area of a rectangle with a width equal to the base of the triangle and length equal to the height of the triangle.</ span >
2647+ < br >
26462648< div style ="margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
2647- < meta itemprop ="position " content =" 1 " >
2649+ < meta itemprop ="position " content =1 >
26482650< span itemprop ="abstract "> The base of a triangle multiplied by its height equals a rectangle with twice the area of the triangle.
2651+ </ div >
26492652< br >
2650- The square root of half of the area of the rectangle is the side length of the theoretical square that has the same area as the triangle.</ span >
2653+ < div style ="margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
2654+ < meta itemprop ="position " content =2 >
2655+ < span itemprop ="abstract "> The square root of half of the area of the rectangle is the side length of the virtual square that has the same area as the triangle.</ span >
26512656</ div >
26522657</ div >
26532658< br >
26542659< div style ="margin:12px " itemprop ="result " itemscope itemtype ="https://schema.org/PropertyValue ">
2655- < meta itemprop ="description " content ="Exact triangle area formula ">
26562660< span itemprop ="name "> A< sub > triangle</ sub > </ span > =
26572661< meta itemprop ="value " content ="base × height / 2 ">
2662+ < meta itemprop ="description " content ="Exact triangle area formula ">
26582663< math xmlns ="http://www.w3.org/1998/Math/MathML ">
26592664< mrow >
26602665< mfrac >
@@ -2756,8 +2761,8 @@ <h3 style="margin:7px" itemprop="name">Area of a Triangle</h3>
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27612766</ div >
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27632768< meta itemprop ="featureList " content ="Calculates the area of a triangle by the length of its sides ">
@@ -2821,6 +2826,7 @@ <h3 style="margin:7px" itemprop="name">Area of a Triangle</h3>
28212826</ section >
28222827< br > < br > < br >
28232828< section itemprop ="mathExpression " itemscope itemtype ="https://schema.org/SolveMathAction " id ="polygon ">
2829+ < h3 itemprop ="name " style ="margin:7px "> Area of a regular Polygon</ h3 >
28242830< meta itemprop ="eduQuestionType " content ="Polygon area calculation ">
28252831< div itemprop ="object " itemscope itemtype ="https://schema.org/QuantitativeValue ">
28262832< meta itemprop ="name " content ="side count ">
@@ -2834,6 +2840,7 @@ <h3 style="margin:7px" itemprop="name">Area of a Triangle</h3>
28342840</ div >
28352841< meta itemprop ="target " content ="https://basic-geometry.github.io?q={polygon_sideCount=8_sideLength=4_area=?} ">
28362842< div itemprop ="actionProcess " itemscope itemtype ="https://schema.org/HowTo ">
2843+ < meta itemprop ="name " content ="Derive the Area of a regular Polygon ">
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@@ -2846,7 +2853,6 @@ <h3 style="margin:7px" itemprop="name">Area of a Triangle</h3>
28462853</ div >
28472854</ div >
28482855< meta itemprop ="totalTime " content ="PT30M ">
2849- < h3 itemprop ="name " style ="margin:7px "> Area of a regular Polygon</ h3 >
28502856< br >
28512857< figure itemprop ="image " class ="imgbox " itemscope itemtype ="https://schema.org/ImageObject ">
28522858 < img class ="center-fit " src ="polygon.png " alt ="A regular polygon can be divided into as many isosceles triangles as many sides it has. ">
@@ -2961,8 +2967,8 @@ <h3 itemprop="name" style="margin:7px">Area of a regular Polygon</h3>
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2965- < meta itemprop ="reviewCount " content =" 1 " >
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29662972</ div >
29672973< meta itemprop ="applicationCategory " content ="Geometric Calculator ">
29682974< meta itemprop ="featureList " content ="Calculates the area of a regular polygon by the number and the length of its sides ">
@@ -3028,33 +3034,37 @@ <h3 itemprop="name" style="margin:7px">Area of a regular Polygon</h3>
30283034</ section >
30293035< br > < br > < br > < br >
30303036< section itemprop ="mathExpression " itemscope itemtype ="https://schema.org/SolveMathAction " id ="circle-segment ">
3037+ < h3 itemprop ="name " style ="margin:7px "> Area of a Circle Segment</ h3 >
30313038< meta itemprop ="eduQuestionType " content ="Circle segment area calculation ">
30323039< div itemprop ="object " itemscope itemtype ="https://schema.org/QuantitativeValue ">
30333040< meta itemprop ="name " content ="height ">
30343041< meta itemprop ="description " content ="segment height ">
3035- < meta itemprop ="minValue " content =" 0 " >
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30363043</ div >
30373044< div itemprop ="object " itemscope itemtype ="https://schema.org/QuantitativeValue ">
30383045< meta itemprop ="name " content ="length ">
30393046< meta itemprop ="description " content ="chord length ">
3040- < meta itemprop ="minValue " content =" 0 " >
3047+ < meta itemprop ="minValue " content =0 >
30413048</ div >
30423049< div itemprop ="object " itemscope itemtype ="https://schema.org/QuantitativeValue ">
30433050< meta itemprop ="name " content ="radius ">
30443051< meta itemprop ="description " content ="radius of the parent circle ">
3045- < meta itemprop ="minValue " content =" 0 " >
3052+ < meta itemprop ="minValue " content =0 >
30463053</ div >
30473054< meta itemprop ="target " content ="https://basic-geometry.github.io?q={circle_segment_height=1_length=3_radius=4_area=?} ">
30483055< div itemprop ="actionProcess " itemscope itemtype ="https://schema.org/HowTo ">
3049- < div itemprop ="estimatedCost " itemscope itemtype ="https://schema.org/MonetaryAmount ">
3056+ < meta itemprop ="name " content ="Derive the Area of a Circle Segment ">
3057+ < div itemprop ="estimatedCost " itemscope itemtype ="https://schema.org/MonetaryAmount ">
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30523060</ div >
30533061< div itemprop ="tool " itemscope itemtype ="https://schema.org/HowToTool ">
3062+ < meta itemprop ="name " content ="Circle area formula ">
30543063< div itemprop ="item " itemscope itemtype ="https://schema.org/PropertyValue ">
3055- < meta itemprop ="description " content ="Exact circle area formula ">
30563064< meta itemprop ="name " content ="Area of a circle ">
30573065< meta itemprop ="value " content ="3.2 × radius^2 ">
3066+ < meta itemprop ="description " content ="Exact formula derived from direct circle to square comparison ">
3067+ < meta itemprop ="disambiguatingDescription " content ="No pi ">
30583068</ div >
30593069</ div >
30603070< div itemprop ="tool " itemscope itemtype ="https://schema.org/HowToTool ">
@@ -3065,7 +3075,6 @@ <h3 itemprop="name" style="margin:7px">Area of a regular Polygon</h3>
30653075</ div >
30663076</ div >
30673077< meta itemprop ="totalTime " content ="PT30M ">
3068- < h3 itemprop ="name " style ="margin:7px "> Area of a Circle Segment</ h3 >
30693078< br >
30703079< figure itemprop ="image " class ="imgbox " itemscope itemtype ="https://schema.org/ImageObject ">
30713080 < img class ="center-fit " src ="circleSegment.png " alt ="Circle segment ">
@@ -3253,8 +3262,8 @@ <h3 itemprop="name" style="margin:7px">Area of a Circle Segment</h3>
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3257- < meta itemprop ="reviewCount " content =" 1 " >
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32583267</ div >
32593268< meta itemprop ="applicationCategory " content ="Geometric Calculator ">
32603269< meta itemprop ="description " content ="Calculates the area of a circle as 3.2×radius^2. ">
@@ -3268,7 +3277,7 @@ <h3 itemprop="name" style="margin:7px">Area of a Circle Segment</h3>
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@@ -3370,24 +3379,26 @@ <h3 itemprop="name" style="margin:7px">Area of a Circle Segment</h3>
33703379</ section >
33713380< br > < br > < br >
33723381< section itemprop ="mathExpression " itemscope itemtype ="https://schema.org/SolveMathAction " id ="pyramid ">
3382+ < h3 itemprop ="name " style ="margin:7px "> Volume of a Pyramid</ h3 >
33733383< meta itemprop ="eduQuestionType " content ="Pyramid volume calculation ">
33743384< div itemprop ="object " itemscope itemtype ="https://schema.org/QuantitativeValue ">
33753385< meta itemprop ="name " content ="sideCount ">
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3386+ < meta itemprop ="minValue " content =3 >
33773387</ div >
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33793389< meta itemprop ="name " content ="baseEdge ">
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3390+ < meta itemprop ="minValue " content =0 >
33813391</ div >
33823392< div itemprop ="object " itemscope itemtype ="https://schema.org/QuantitativeValue ">
33833393< meta itemprop ="name " content ="height ">
3384- < meta itemprop ="minValue " content =" 0 " >
3394+ < meta itemprop ="minValue " content =0 >
33853395</ div >
33863396< meta itemprop ="target " content ="https://basic-geometry.github.io?q={pyramid_bottom_edge_number=5_length=3_height=2_volume=?} ">
33873397< div itemprop ="actionProcess " itemscope itemtype ="https://schema.org/HowTo ">
3398+ < meta itemprop ="name " content ="Derive the Volume of a Pyramid ">
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3390- < meta itemprop ="value " content =" 0 " >
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33913402</ div >
33923403< div itemprop ="tool " itemscope itemtype ="https://schema.org/HowToTool ">
33933404< meta itemprop ="name " content ="Cone volume formula ">
@@ -3399,13 +3410,12 @@ <h3 itemprop="name" style="margin:7px">Area of a Circle Segment</h3>
33993410</ div >
34003411</ div >
34013412< div itemprop ="tool " itemscope itemtype ="https://schema.org/HowToTool ">
3402- < meta itemprop ="name " content ="Polygon area formula ">
3413+ < meta itemprop ="name " content ="Regular polygon area formula ">
34033414< div itemprop ="item " itemscope itemtype ="https://schema.org/PropertyValue ">
34043415< meta itemprop ="name " content ="Area of a regular polygon ">
34053416< meta itemprop ="value " content ="sideCount / 4 × ctg( 180° / sideCount ) × sideLength^2 ">
34063417</ div >
34073418</ div >
3408- < h3 itemprop ="name " style ="margin:7px "> Volume of a Pyramid</ h3 >
34093419< br >
34103420< figure itemprop ="image " class ="imgbox " itemscope itemtype ="https://schema.org/ImageObject ">
34113421 < img class ="center-fit " src ="conePyramidVolume.jpeg " alt ="Pyramid ">
@@ -3448,9 +3458,9 @@ <h3 itemprop="name" style="margin:7px">Volume of a Pyramid</h3>
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34493459< meta itemprop ="position " content ="1 ">
34503460< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
3451- < meta itemprop ="description " content ="Exact cone volume formula ">
34523461< span itemprop ="name "> V< sub > cone</ sub > </ span > =
34533462< meta itemprop ="value " content ="base area × height / 8^(1/2) ">
3463+ < meta itemprop ="description " content ="Exact cone volume formula ">
34543464< math xmlns ="http://www.w3.org/1998/Math/MathML ">
34553465< mrow >
34563466< mfrac >
@@ -3473,9 +3483,9 @@ <h3 itemprop="name" style="margin:7px">Volume of a Pyramid</h3>
34733483</ div >
34743484< br >
34753485< div style ="margin:12px " itemprop ="result " itemscope itemtype ="https://schema.org/PropertyValue ">
3476- < meta itemprop ="description " content ="Exact pyramid volume formula ">
34773486< span itemprop ="name "> V< sub > pyramid</ sub > </ span > =
34783487< meta itemprop ="value " content ="base area × height / 8^(1/2) ">
3488+ < meta itemprop ="description " content ="Exact pyramid volume formula ">
34793489< math xmlns ="http://www.w3.org/1998/Math/MathML ">
34803490< mrow >
34813491< mfrac >
@@ -3503,8 +3513,8 @@ <h3 itemprop="name" style="margin:7px">Volume of a Pyramid</h3>
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35083518</ div >
35093519< meta itemprop ="applicationCategory " content ="Geometric Calculator ">
35103520< meta itemprop ="description " content ="Calculates the volume of a pyramid as base×height/8^(1/2). ">
@@ -3518,7 +3528,7 @@ <h3 itemprop="name" style="margin:7px">Volume of a Pyramid</h3>
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