✏️ Activities 1 & 2 — Student Worksheet Page

Type your answers in the boxes. Instead of Л write pi. For powers, use plain text like r^2 (instead of r²). If you need to write something like “x to a power,” you can type it directly (example: x^3).

1.1 — Area Under a Line (Triangle)

Area of the shaded region (numeric):

Example format: 9.42 or (1/2)*base*height

Area of the shaded region (in terms of r):

Example: r^2/2

1.2 — Area Under a Line (Triangle)

Area of the shaded region (numeric):

Example: (1/2)*12*12

Area of the shaded region (in terms of r):

Common form: r^2/2

2.1 — Find the Area of the Shaded Trapezoid

Do this for both pictures: compute Area of rectangle and Area of triangle, then add to get the Total Area.

Left picture

Area of rectangle: Area of triangle: Total Area (rectangle + triangle):

Right picture

Area of rectangle: Area of triangle: Total Area (rectangle + triangle):

Write the total area as a function of x (plain text):

Example: A(x)=x^2/2 + 2x

2.2 — Tables First, Then Slope at x = 2

Step 1: Complete both tables. Put the tables side-by-side so you can compare them easily.

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) = x^2/2 + 2x
0
1
2
3

Step 2: After you fill the tables, answer this:

Explain (1–3 sentences): How does the area under the line relate to A(x)?

Step 3: Look at the graph below and estimate the slope at x=2.

Slope question

Estimate the slope at x = 2 (rise/run):

Example format: rise/run = (y2-y1)/(x2-x1)