Polygon Area Explorer — Worksheet

Polygon Area Explorer

Worksheet

Open the Polygon Area Explorer. Choose a shape with the buttons, and press Reset shape if you move a vertex by accident. Vertices sit on grid points, so the coordinates are whole numbers.

Name: Date:

Part A: Triangles and rectangles

1. Choose the Triangle. Its base runs along the bottom from (−4, −3) to (4, −3). What is the base length? 1 pt
Answer:
2. For the same triangle, what is the height h shown by the dashed line? 1 pt
Answer:
3. Use A = ½ × b × h. What is the area of this triangle? 1 pt
Answer:
4. Choose the Rectangle. Use A = l × w. What is its area? 1 pt
Answer:
5. On the rectangle, the top side runs from (−4, 3) to (4, 3). Use the x-coordinates to find its length. 1 pt
Answer:

Part B: Parallelograms and trapezoids

6. Choose the Parallelogram. The base runs from (−4, −2) to (2, −2). What is the base length? 1 pt
Answer:
7. Use A = b × h for the parallelogram. What is its area? 1 pt
Answer:
8. Choose the Trapezoid. The top base runs from (−3, 3) to (2, 3). What is the top base length (b₂)? 1 pt
Answer:
9. Use A = ½ × (b₁ + b₂) × h. The bottom base b₁ is 9 and the height is 5. What is the area of the trapezoid? 1 pt
Answer:

Part C: Decomposing

10. Choose the Quadrilateral and turn on Decompose. The two triangles have areas 21 and 13. What is the area of the whole quadrilateral? 1 pt
  • 21 square units
  • 34 square units
  • 26 square units
  • 44 square units
11. Why does splitting a polygon into triangles help you find its area? Explain using the quadrilateral. 2 pts