Stage 3 · Geometry

L-Shapes & Composite Rectangles

L-shapes and composite figures appear constantly on the GED — in floor plans, yards, rooms, and patios. The key skill is always the same: find the missing side, break the shape into rectangles, then calculate.

📖 Review — Area & Perimeter of Rectangles

Area

A = length × width

Perimeter

P = sum of all sides

What Is a Composite Shape?

A composite shape is made of two or more rectangles combined. L-shapes are the most common type on the GED. They look like a rectangle with a corner cut out.

Step 1 — Find Both Missing Sides

Every L-shape hides at least two side lengths — one horizontal and one vertical. You must find both before you can calculate the area or perimeter. Use the opposite parallel side to figure out what's missing.

The rule: Opposite parallel sides must add up to the same total.
If the full width is 10 ft and one part is 4 ft, the missing part is 10 − 4 = 6 ft.
If the full height is 8 ft and one part is 3 ft, the missing part is 8 − 3 = 5 ft.

Finding Both Missing Sides

→ Missing horizontal: 12 − 4 = 8 ft

→ Missing vertical: 8 − 3 = 5 ft

Both missing sides found ✓

Step 2 — Find the Area

Use the subtract method: imagine the full rectangle, calculate its area, then subtract the missing corner.

Find both missing sides — always do this first

Full rectangle area — outer length × outer width

Cutout area — the missing corner piece

Subtract — full area − cutout = L-shape area

Worked Example — Area & Perimeter

L-shape: 10 ft wide, 8 ft tall. Cutout: 4 ft wide, 3 ft tall (top-right corner).

→ Missing horizontal: 12 − 4 = 8 ft

→ Missing vertical: 8 − 3 = 5 ft

→ Full rectangle: 12 × 8 = 96 sq ft

→ Cutout: 4 × 3 = 12 sq ft

→ Area = 80 − 12 = 68 sq ft

→ Perimeter: trace all 6 outer edges: 12 + 8 + 4 + 3 + 8 + 5 = 40 ft

→ Shortcut: 2 × (12 + 8) = 40 ft

Area = 68 sq ft | Perimeter = 40 ft

Finding Perimeter

For perimeter, trace all the outer edges only. Do not include any interior lines. An L-shape has exactly 6 outer sides — and you need all the missing sides to count them all.

Shortcut: The perimeter of any L-shape = 2 × (full width + full height). The notch adds two new sides but removes two equal sides — they cancel out exactly.

Common mistakes:
• Forgetting to find the missing side before calculating
• Including interior lines when finding perimeter
• Using the cutout dimensions for the whole shape's area
• Mixing up square feet (area) and feet (perimeter)

🎯 Test Strategy — Estimate First, Eliminate Fast

1.Look at the answer choices first. If the full rectangle would be 120 sq ft, the L-shape must be less than 120. Eliminate anything larger.

2.Find the missing side before anything else. Every L-shape problem hides at least one dimension — get that first or everything else is wrong.

3.For cost problems — multiply area by cost per square foot last. Get the area right first, then multiply.

4.Watch the units — area is always in square feet (sq ft), perimeter is just feet (ft).

Reference

GED Formula Sheet

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📋 Open Formula Sheet

✏️ Practice Questions

Bank 1 — L-Shapes: Area & Perimeter

Find the missing side, then calculate. Mix of multiple choice and fill-in.

You've answered 5 questions. Keep going or check your score.

Bank 2 — Real-World Applications

Carpet, tile, grass, pavers — find the area then calculate cost.

You've answered 5 questions. Keep going or check your score.

Up Next in Stage 3

Missing Side Lengths

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