💡 What You Will Learn
On the GED, a figure is drawn on a grid where each small square = 1 square unit. You need to find the area (count shaded squares) and the perimeter (count exposed edges on the border). The key GED skill is identifying which shape satisfies both a given area AND a given perimeter!
Area = total number of shaded (filled) squares
Each small grid square = 1 square unit
For a rectangle: Area = width × height (faster than counting one by one)
All the colored/shaded squares inside the figure count.
Count them one by one, OR use the formula: A = rows × columns for rectangles.
A 2×4 rectangle has 8 shaded squares → Area = 8 square units.
Area = width × height
4 columns × 2 rows = 8 square units ✅
For L-shapes, T-shapes, or any non-rectangular figure, count each shaded square individually.
Perimeter = total number of unit-length edges on the outside border of the figure.
Key: an edge shared between two shaded squares is NOT on the perimeter — only edges that face the outside (or the unshaded area) count!
Trace the outer boundary of all shaded squares together.
Each step along the boundary = 1 unit. Count every edge segment.
P = 2 × (width + height)
2×4 rectangle: P = 2×(4+2) = 2×6 = 12 units ✅
P = 2 × (length + width)
A 4×2 rectangle: 2 × (4 + 2) = 2 × 6 = 12 units
A 3×3 square: 2 × (3 + 3) = 2 × 6 = 12 units
Both have the SAME perimeter but different areas!
A figure is formed by shaded squares on a grid (1 square = 1 square unit). Which figure has a perimeter of 12 units and an area of 8 square units?
| Shape | Dimensions | Area | Perimeter | Both Match? |
|---|---|---|---|---|
| A — 3×4 rectangle | 3 wide × 4 tall | 12 sq units | 14 units | ❌ No |
| B — 2×4 rectangle | 2 wide × 4 tall | 8 sq units | 12 units | ❌ Wait— |
| C — 2×4 rectangle ✅ | 2 wide × 4 tall | 8 sq units ✅ | 12 units ✅ | ✅ CORRECT |
| D — 3×3 square | 3 wide × 3 tall | 9 sq units | 12 units | ❌ No |
Perimeter = 2 × (2 + 4) = 2 × 6 = 12 units ✅
Both conditions satisfied!
A 3×3 square and a 2×4 rectangle BOTH have perimeter = 12. But their areas differ: 3×3 = 9 sq units, 2×4 = 8 sq units. You must check BOTH conditions! Don't stop after finding one match.
Whether it's a rectangle, L-shape, or T-shape, count every shaded square. Area = total shaded squares.
Walk along the outside edge and count every unit-length segment. Don't count interior lines shared between two shaded squares.
A 6-square L-shape usually has a LARGER perimeter than a 6-square straight rectangle, because it has more "corners" and exposed edges.
| Shape | Area | Perimeter |
|---|---|---|
| 1×8 rectangle | 8 sq units | 18 units |
| 2×4 rectangle | 8 sq units | 12 units ✅ |
| 4×2 rectangle | 8 sq units | 12 units ✅ |
| 3×3 square (9 sq) | 9 sq units | 12 units |
| 2×6 rectangle | 12 sq units | 16 units |
Width=4, Height=2 → Area=8, Perimeter=12 (the GED answer!)
Width=3, Height=3 → Area=9, Perimeter=12 (same perimeter, different area!)
Width=1, Height=8 → Area=8, Perimeter=18 (same area, much bigger perimeter!)
Many shapes may match one condition (area OR perimeter). You need the shape that satisfies BOTH at the same time. Don't stop early!
A 2×4 rectangle: 2 rows × 4 columns = 8 squares. Much faster than counting 1 by 1.
Use a pencil to trace the outer edge and count each unit step. OR use P = 2(l + w) for rectangles.
A 3×3 and a 2×4 both have P=12. But 3×3 has area=9, and 2×4 has area=8. These are different figures!
For an L-shape, trace every unit of the outer border. Inner corners add extra border — don't miss them!
| Measurement | Grid Method | Formula (rectangles) |
|---|---|---|
| Area | Count all shaded squares | A = w × h |
| Perimeter | Count all outer border edges | P = 2(w + h) |