Adventure 1 — Activity 2 (Solution)

These boxes are filled with the answers shown on the solution pages. Use them to check your work and to see the pattern: area under a line becomes a function, and the slope becomes a derivative.

1️⃣ Page 1 — Area Under a Line (Triangles)

1.1 Area of shaded region (numeric): 1.1 Area of shaded region (in terms of r):

1.2 Area of shaded region (numeric): 1.2 Area of shaded region (in terms of r):

2️⃣ Page 2 — Trapezoids, Tables, and Slope at x = 2

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.

2.1 Left picture — area of rectangle: 2.1 Left picture — area of triangle: 2.1 Left picture — total area:

2.1 Right picture — area of rectangle: 2.1 Right picture — area of triangle: 2.1 Right picture — total area:

Write the total area as a function of x:

Table A — Area of the trapezoid at x

x	Area of the Trapezoid at x
0
1
2
3

Table B — Values of A(x) = x^2/2 + 2x

x	A(x)
0
1
2
3

2.2 Explanation (example): 2.2 Slope at x = 2: