// Numbas version: finer_feedback_settings {"name": "john's copy of Calculate the areas of polygons", "extensions": [], "custom_part_types": [], "resources": [["question-resources/trapezium.svg", "trapezium.svg"], ["question-resources/trangle.svg", "trangle.svg"], ["question-resources/parallelogram.svg", "parallelogram.svg"], ["question-resources/Parallelogram_area_animated.gif", "Parallelogram_area_animated.gif"], ["question-resources/rectangle_zISmvoz.svg", "rectangle_zISmvoz.svg"], ["question-resources/hardertrapezium_8GqMwOo.svg", "hardertrapezium_8GqMwOo.svg"], ["question-resources/Trap_advice.svg", "Trap_advice.svg"], ["question-resources/Triangle_advice_lD6eKvD.svg", "Triangle_advice_lD6eKvD.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "name": "john's copy of Calculate the areas of polygons", "functions": {}, "ungrouped_variables": [], "statement": "

Calculate the area of the following shapes.

", "variables": {"h5": {"description": "

Height of the trapezium.

", "definition": "random(2..5#0.1)", "templateType": "anything", "group": "'Harder' trapezium", "name": "h5"}, "w5a": {"description": "

The top parallel side in the trapezium.

", "definition": "random(5..6.5#0.1)", "templateType": "anything", "group": "'Harder' trapezium", "name": "w5a"}, "wh11": {"description": "

The product of the two terms, w1 and h1, such that a condition can be satisfied.

", "definition": "precround(w1*h1,3)", "templateType": "anything", "group": "Parallelogram", "name": "wh11"}, "wh11dp": {"description": "

The product of the two terms, w1 and h1, to one decimal place such that a condition can be satisfied.

", "definition": "precround(w1*h1, 1)", "templateType": "anything", "group": "Parallelogram", "name": "wh11dp"}, "wabh5dp": {"description": "

The Area of a trapezium using the three terms, w5a, w5b and h5 to one decimal place, such that a condition can be satisfied.

", "definition": "precround((w5a+w5b)*(h5)/2, 1)", "templateType": "anything", "group": "'Harder' trapezium", "name": "wabh5dp"}, "wh00": {"description": "

The product of the two terms, w0 and h0, such that a condition can be satisfied.

", "definition": "precround(w0*h0,3)", "templateType": "anything", "group": "Rectangle", "name": "wh00"}, "h2": {"description": "

Height of the triangle.

", "definition": "random(1..4.5#0.1)", "templateType": "anything", "group": "Triangle", "name": "h2"}, "h1": {"description": "

The height of the parallelogram

", "definition": "random(1..4.5#0.1)", "templateType": "anything", "group": "Parallelogram", "name": "h1"}, "wabh5": {"description": "

The Area of a trapezium using the three terms, w5a, w5b and h5, such that a condition can be satisfied.

", "definition": "precround((w5a+w5b)*(h5)/2, 5)", "templateType": "anything", "group": "'Harder' trapezium", "name": "wabh5"}, "wh22": {"description": "

The Area of a triangle using the two terms, w2 and h2, such that a condition can be satisfied.

", "definition": "precround(0.5*w2*h2,4)", "templateType": "anything", "group": "Triangle", "name": "wh22"}, "w0": {"description": "

Width of the rectangle.

", "definition": "random(5..10#0.1)", "templateType": "anything", "group": "Rectangle", "name": "w0"}, "w1": {"description": "

The width of the parallelogram.

", "definition": "random(5..10#0.1)", "templateType": "anything", "group": "Parallelogram", "name": "w1"}, "w2": {"description": "

Base of the triangle.

", "definition": "random(5..10#0.1)", "templateType": "anything", "group": "Triangle", "name": "w2"}, "wh00dp": {"description": "

The product of the two terms, w0 and h0, to one decimal place, such that a condition can be satisfied.

", "definition": "precround(w0*h0,1)", "templateType": "anything", "group": "Rectangle", "name": "wh00dp"}, "wh22dp": {"description": "

The Area of a triangle using the two terms, w2 and h2 to one decimal place, such that a condition can be satisfied.

", "definition": "precround(0.5*w2*h2, 1)", "templateType": "anything", "group": "Triangle", "name": "wh22dp"}, "h0": {"description": "

Height of the rectangle.

", "definition": "random(1..5#0.1)", "templateType": "anything", "group": "Rectangle", "name": "h0"}, "w5b": {"description": "

The bottom parallel side in the trapezium.

", "definition": "random(7.5..10#0.1)", "templateType": "anything", "group": "'Harder' trapezium", "name": "w5b"}}, "advice": "

The area of a rectangle is calculated using the formula

\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}\\text{.}\\]

We have a base of $\\var{w0}$m and a height $\\var{h0}$m, therefore

\\begin{align}
\\mathrm{Area} &= \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\var{w0} \\times \\var{h0} \\\\ &= \\var{w0*h0} \\\\
&= \\var{dpformat(w0*h0,1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}

\\begin{align}
\\mathrm{Area} &= \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\var{w0} \\times \\var{h0} \\\\
&= \\var{dpformat(w0*h0,1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}

The parallelogram is just a slanted rectangle:

$\"Parallelogram\"$

Animation by Picknick.

Therefore, the area of a parallelogram is calculated using the formula

\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}.\\]

We have a base $\\var{w1}$m and perpendicular height $\\var{h1}$m.

\\begin{align}
\\mathrm{Area} &= \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\var{w1} \\times \\var{h1} \\\\ &= \\var{{w1}{h1}}\\, \\mathrm{m}^2 \\\\
&= \\var{dpformat({w1}{h1},1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}

\\begin{align}
\\mathrm{Area} &= \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\var{w1} \\times \\var{h1} \\\\
&= \\var{dpformat({w1}{h1},1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}

c)

The area of a triangle is calculated using the formula

\\[\\mathrm{Area} = \\frac{\\mathrm{base} \\times \\mathrm{height}}{2}.\\]

Note that the triangle is half of a rectangle:

Our triangle has a base $\\var{w2}$m and a height $\\var{h2}$m, therefore

\\begin{align} \\mathrm{Area} &= \\frac{1}{2} \\times \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\frac{1}{2} \\times \\var{w2} \\times \\var{h2} \\\\
&= \\var{0.5*w2*h2}\\, \\mathrm{m}^2 \\\\
&= \\var{dpformat(0.5*w2*h2, 1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}

\\begin{align} \\mathrm{Area} &= \\frac{1}{2} \\times \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\frac{1}{2} \\times \\var{w2} \\times \\var{h2} \\\\
&= \\var{dpformat(0.5*w2*h2, 1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}

A trapezium can be interpreted as half of a parallelogram, this is shown below:

As we only want the area of one half of this shape, the area is half of

\\[\\mathrm{area} = (a+b) \\times \\mathrm{height}\\text{,}\\]

with ${a} = \\var{w5a}$m, ${b} = \\var{w5b}$m, and height $\\var{h5}$m.

\\begin{align}
\\mathrm{Area} &= \\frac{(a+b)}{2} \\times \\mathrm{height} \\\\
&= \\frac{(\\var{w5a}+\\var{w5b})}{2} \\times \\var{h5} \\\\
&= \\var{(w5a+w5b)*0.5} \\times \\var{h5} \\\\
&= \\var{(w5a+w5b)*(h5)/2}\\, \\mathrm{m}^2 \\\\
&= \\var{dpformat((w5a+w5b)*(h5)/2, 1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.}
\\end{align}

\\begin{align}
\\mathrm{Area} &= \\frac{(a+b)}{2} \\times \\mathrm{height} \\\\
&= \\frac{(\\var{w5a}+\\var{w5b})}{2} \\times \\var{h5} \\\\
&= \\var{(w5a+w5b)*0.5} \\times \\var{h5} \\\\
&= \\var{dpformat((w5a+w5b)*(h5)/2, 1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.}
\\end{align}

", "extensions": [], "variable_groups": [{"name": "Parallelogram", "variables": ["h1", "w1", "wh11", "wh11dp"]}, {"name": "Triangle", "variables": ["h2", "w2", "wh22", "wh22dp"]}, {"name": "'Harder' trapezium", "variables": ["h5", "w5a", "w5b", "wabh5dp", "wabh5"]}, {"name": "Rectangle", "variables": ["w0", "h0", "wh00", "wh00dp"]}], "rulesets": {}, "tags": ["area", "Area", "area of a parallelogram", "area of a rectangle", "area of a right-angled triangle", "area of a trapezium", "parallelogram", "Rectangle", "rectangle", "right - angled triangle", "shapes", "taxonomy", "trapezium"], "metadata": {"description": "

This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

Author of gif: Picknick
https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"gaps": [{"maxValue": "{h0}{w0}", "precisionType": "dp", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{h0}{w0}", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "precision": "1", "precisionMessage": "You have not given your answer to the correct precision.", "marks": "2", "correctAnswerFraction": false, "type": "numberentry", "precisionPartialCredit": 0, "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "strictPrecision": false, "showCorrectAnswer": true}], "type": "gapfill", "prompt": "

The area of the rectangle is [[0]] $\\mathrm{m^2}$. Round your answer to 1 decimal place.

", "marks": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "stepsPenalty": "1", "steps": [{"marks": 0, "type": "information", "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "

The formula for the area of a rectangle is:

\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}.\\]

", "variableReplacements": []}], "variableReplacements": []}, {"gaps": [{"maxValue": "{h1}*{w1} + 0.01", "precisionType": "dp", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{h1}*{w1} - 0.01", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "precision": "1", "precisionMessage": "You have not given your answer to the correct precision.", "marks": "2", "correctAnswerFraction": false, "type": "numberentry", "precisionPartialCredit": 0, "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "strictPrecision": false, "showCorrectAnswer": true}], "type": "gapfill", "prompt": "

The area of the parallelogram is [[0]] $\\mathrm{m^2}$. Round your answer to 1 decimal place.

The formula for the area of a parallelogram is:

\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}.\\]

", "variableReplacements": []}], "variableReplacements": []}, {"gaps": [{"maxValue": "{w2}{h2}*0.5 + 0.01", "precisionType": "dp", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{w2}{h2}*0.5 - 0.01", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "precision": "1", "precisionMessage": "You have not given your answer to the correct precision.", "marks": "2", "correctAnswerFraction": false, "type": "numberentry", "precisionPartialCredit": 0, "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "strictPrecision": false, "showCorrectAnswer": true}], "type": "gapfill", "prompt": "

The area of the triangle is [[0]] $\\mathrm{m^2}$ Round your answer to 1 decimal place.

The formula for the area of a triangle is:

\\[\\mathrm{Area} = \\frac{\\mathrm{base} \\times \\mathrm{height}}{2}.\\]

", "variableReplacements": []}], "variableReplacements": []}, {"gaps": [{"maxValue": "0.5{w5a+w5b}{h5} + 0.01", "precisionType": "dp", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "0.5{w5a+w5b}{h5} - 0.01", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "precision": "1", "precisionMessage": "You have not given your answer to the correct precision.", "marks": "2", "correctAnswerFraction": false, "type": "numberentry", "precisionPartialCredit": 0, "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "strictPrecision": false, "showCorrectAnswer": true}], "type": "gapfill", "prompt": "

The area of the trapezium is [[0]] $\\mathrm{m^2}$. Round your answer to 1 decimal place.

The formula for the area of a trapezium is:

\\[\\mathrm{Area} = \\frac{(a+b)}{2}\\times \\mathrm{height}.\\]

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