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<title>Adventure 1 โ Activity 2 (Solution)</title>
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<h1>Adventure 1 โ Activity 2 (Solution)</h1>
<p class="hint">
These boxes are filled with the answers shown on the solution pages. Use them to check your work and to see the pattern:
<strong>area under a line</strong> becomes a function, and the <strong>slope</strong> becomes a derivative.
</p>
<h2>1๏ธโฃ Page 1 โ Area Under a Line (Triangles)</h2>
<div class="card">
<div class="imgwrap">
<img src="images/adventure_1_image_2.1_solution.png" alt="Activity 2 solution page 1">
</div>
<div class="row-grid">
<div>
<label for="a11_area_num">1.1 Area of shaded region (numeric):</label>
<input id="a11_area_num" type="text" value="9ะ" readonly class="correct">
<label for="a11_area_r">1.1 Area of shaded region (in terms of r):</label>
<input id="a11_area_r" type="text" value="ะr^2" readonly class="correct">
</div>
<div>
<label for="a12_area_num">1.2 Area of shaded region (numeric):</label>
<input id="a12_area_num" type="text" value="72" readonly class="correct">
<label for="a12_area_r">1.2 Area of shaded region (in terms of r):</label>
<input id="a12_area_r" type="text" value="r^2/2" readonly class="correct">
</div>
</div>
</div>
<h2>2๏ธโฃ Page 2 โ Trapezoids, Tables, and Slope at x = 2</h2>
<div class="card">
<div class="imgwrap">
<img src="images/adventure_1_image_2.2_solution.png" alt="Activity 2 solution page 2">
</div>
<p class="hint">
For the left trapezoid picture (the specific x = 2 picture), split the region into a rectangle and a triangle.
For the right trapezoid picture, write each part using x.
</p>
<div class="row-grid">
<div>
<label for="a21_left_rect">2.1 Left picture โ area of rectangle:</label>
<input id="a21_left_rect" type="text" value="4" readonly class="correct">
<label for="a21_left_tri">2.1 Left picture โ area of triangle:</label>
<input id="a21_left_tri" type="text" value="2" readonly class="correct">
<label for="a21_left_total">2.1 Left picture โ total area:</label>
<input id="a21_left_total" type="text" value="6" readonly class="correct">
</div>
<div>
<label for="a21_right_rect">2.1 Right picture โ area of rectangle:</label>
<input id="a21_right_rect" type="text" value="2x" readonly class="correct">
<label for="a21_right_tri">2.1 Right picture โ area of triangle:</label>
<input id="a21_right_tri" type="text" value="x^2/2" readonly class="correct">
<label for="a21_right_total">2.1 Right picture โ total area:</label>
<input id="a21_right_total" type="text" value="x^2/2 + 2x" readonly class="correct">
</div>
</div>
<div style="margin-top:0.8rem;">
<label for="a21_formula"><strong>Write the total area as a function of x:</strong></label>
<input id="a21_formula" type="text" value="A(x)=x^2/2 + 2x" readonly class="correct">
</div>
<div class="row-grid" style="margin-top:0.9rem;">
<div>
<h3 style="margin:0.2rem 0 0.25rem;">Table A โ Area of the trapezoid at x</h3>
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<table>
<thead><tr><th>x</th><th>Area of the Trapezoid at x</th></tr></thead>
<tbody>
<tr><td>0</td><td><input type="text" id="tA0" value="0" readonly class="correct"></td></tr>
<tr><td>1</td><td><input type="text" id="tA1" value="2.5" readonly class="correct"></td></tr>
<tr><td>2</td><td><input type="text" id="tA2" value="6" readonly class="correct"></td></tr>
<tr><td>3</td><td><input type="text" id="tA3" value="10.5" readonly class="correct"></td></tr>
</tbody>
</table>
</div>
</div>
<div>
<h3 style="margin:0.2rem 0 0.25rem;">Table B โ Values of A(x) = x^2/2 + 2x</h3>
<div class="tablewrap">
<table>
<thead><tr><th>x</th><th>A(x)</th></tr></thead>
<tbody>
<tr><td>0</td><td><input type="text" id="tB0" value="0" readonly class="correct"></td></tr>
<tr><td>1</td><td><input type="text" id="tB1" value="2.5" readonly class="correct"></td></tr>
<tr><td>2</td><td><input type="text" id="tB2" value="6" readonly class="correct"></td></tr>
<tr><td>3</td><td><input type="text" id="tB3" value="10.5" readonly class="correct"></td></tr>
</tbody>
</table>
</div>
</div>
</div>
<div style="margin-top:0.9rem;">
<label for="a22_explain">2.2 Explanation (example):</label>
<input id="a22_explain" type="text"
value="The area under y=x+2 from 0 to x equals A(x)=x^2/2+2x." readonly class="correct">
<label for="a22_slope" style="margin-top:0.7rem;">2.2 Slope at x = 2:</label>
<input id="a22_slope" type="text" value="4" readonly class="correct">
</div>
</div>
</div>
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