Perimeter Area Worksheet - Free Printable

Explanation:
Let’s solve each shape one by one. Remember:

- Perimeter = total distance around the shape (add all side lengths).
- Area = space inside the shape.

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Shape 1: Rectangle (17 in by 20 in)
- Area = length × width = 17 in × 20 in = 340 in²
- Perimeter = 2 × (length + width) = 2 × (17 + 20) = 2 × 37 = 74 in

✔ Double-check: 17+20+17+20 = 74 ✔️

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Shape 2: Right triangle (legs 15 cm and 25 cm, hypotenuse 30 cm)
We’re told the three sides are 15 cm, 25 cm, and 30 cm. Let’s verify it’s a right triangle using Pythagoras:
15² + 25² = 225 + 625 = 850
30² = 900 → Not equal! So it’s *not* a right triangle — but that’s okay; we don’t need to assume it is. The problem gives all three sides, so we can compute area using base and height *only if* the two shorter sides are perpendicular.

But look: the diagram shows a right angle at the corner where 15 cm and 25 cm meet — that’s standard for such diagrams unless marked otherwise. So assume 15 cm and 25 cm are the legs (perpendicular), and 30 cm is the hypotenuse (even if slightly off due to rounding or drawing approximation — common in worksheets).

So:
- Area = (1/2) × base × height = 0.5 × 15 cm × 25 cm = 187.5 cm²
- Perimeter = 15 + 25 + 30 = 70 cm

✔ Check perimeter: 15+25+30 = 70 ✔️

(If you’re strict about Pythagoras, 15–25–30 isn’t exact, but worksheets like this expect you to use the given legs as base & height.)

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Shape 3: L-shaped figure (in feet)
Given sides: top horizontal = 18 ft, right vertical = 10 ft, bottom left vertical = 8 ft, bottom horizontal = 10 ft. The missing inner horizontal segment (between the “step”) is: 18 ft − 10 ft = 8 ft (since top is 18 ft, bottom left part is 10 ft, so the step sticks out 8 ft).
The missing inner vertical segment is: 10 ft − 8 ft = 2 ft (right side is 10 ft tall, left lower part is 8 ft, so the step rises 2 ft).

To find area, split into two rectangles:
- Bottom rectangle: 10 ft (width) × 8 ft (height) = 80 ft²
- Top rectangle: 18 ft (width) × 2 ft (height) = 36 ft²
→ Total area = 80 + 36 = 116 ft²

Alternative: Big rectangle (18 × 10 = 180 ft²) minus missing rectangle (8 × 2 = 16 ft²) → 180 − 16 = 116 ft² ✔️

For perimeter, walk around the outside:
Start top-left → right 18 ft → down 10 ft → left 8 ft → up 2 ft → left 10 ft → up 8 ft → back to start? Wait — better to list all outer edges:

From top-left corner:
1. Right: 18 ft
2. Down: 10 ft
3. Left: 8 ft (the bottom of the “step” part)
4. Up: 2 ft (the inner vertical step)
5. Left: 10 ft (bottom horizontal)
6. Up: 8 ft (left side)

Wait — that’s not correct. Let’s draw coordinates:

Let bottom-left corner be (0,0).
Then:
- Bottom-left: (0,0)
- Bottom-right of lower rectangle: (10,0)
- Inner corner (step): (10,8)
- Top-right: (18,8)
- Top-left: (0,10) — because total height is 10 ft on right side, and left side goes up to 10 ft.

Wait — actually, from diagram: left side is 10 ft tall (vertical), bottom is 10 ft, then a step up 8 ft, then right 18 ft, then down 10 ft.

Better method: Use the “outline” method — add all outer side lengths shown or implied.

Given labeled sides:
- Left vertical: 10 ft
- Bottom horizontal: 10 ft
- Inner vertical (up from bottom step): 8 ft
- Inner horizontal (top of step): 18 ft
- Right vertical: 10 ft
- Top horizontal: ?

Actually, looking at standard L-shape with those labels:
The full width is 18 ft (top), full height is 10 ft (right side), bottom width is 10 ft, and the “step” height is 8 ft (so the left part is 8 ft tall), meaning the top part sticks out 18 − 10 = 8 ft to the right, and the right part sticks up 10 − 8 = 2 ft.

So outer perimeter path:
- Start at bottom-left (0,0)
- Right to (10,0) → 10 ft
- Up to (10,8) → 8 ft
- Right to (18,8) → 8 ft
- Up to (18,10) → 2 ft
- Left to (0,10) → 18 ft
- Down to (0,0) → 10 ft

Add them: 10 + 8 + 8 + 2 + 18 + 10 = 56 ft

✔ Perimeter = 56 ft
Area we already got: 116 ft²

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Shape 4: Larger L-shape (in meters)
Labels:
- Top horizontal: 70 m
- Left vertical (upper part): 15 m
- Inner horizontal (step bottom): 40 m
- Right vertical (full height): 70 m

We need to infer missing sides.

Total height = 70 m (right side). Upper left part is 15 m tall, so the lower part (below the step) must be 70 − 15 = 55 m tall.

Total width = 70 m (top). Inner horizontal step is 40 m, so the right “arm” width = 70 − 40 = 30 m.

Now, draw coordinates:
- Bottom-left: (0,0)
- Bottom-right: (70,0)
- Top-right: (70,70)
- Top-left: (0,70)
But there’s a cut-out: from (40,15) to (70,15) is missing? Wait — better: The shape looks like a big rectangle 70 m × 70 m, with a rectangular piece removed from the lower-left? No — based on labels: top is 70 m, left upper is 15 m, then a horizontal 40 m inward, then down to bottom (70 m tall on right), so the missing part is a rectangle of width = 70 − 40 = 30 m, and height = 70 − 15 = 55 m? Let's reconstruct:

Standard interpretation for this L-shape:
- Outer rectangle would be 70 m wide × 70 m tall.
- A rectangle is cut out from the bottom-left: width = 40 m? No — the inner horizontal segment is 40 m, which is the bottom of the top bar.

Actually, easier: Break into two rectangles:
1. Top rectangle: width = 70 m, height = 15 m → area = 70 × 15 = 1050 m²
2. Right rectangle (below top bar): width = 70 − 40 = 30 m, height = 70 − 15 = 55 m → area = 30 × 55 = 1650 m²

Total area = 1050 + 1650 = 2700 m²

Check another way: Full big rectangle 70 × 70 = 4900 m²
Minus missing rectangle: width = 40 m, height = 55 m? Wait — missing part is bottom-left: from x=0 to x=40, y=0 to y=55? But left side only shows 15 m on top, so the lower left part is missing — yes, the missing rectangle is 40 m wide and 55 m tall → 40 × 55 = 2200 m²
Then 4900 − 2200 = 2700 m² ✔️

Now perimeter: Walk around outer edges:
- Top: 70 m
- Right side: 70 m
- Bottom: 70 m
- Left side: only 15 m (top part), then a horizontal step inward 40 m, then down 55 m — but that’s inner. For outer perimeter, we go:
Start top-left (0,70):
1. Right to (70,70) → 70 m
2. Down to (70,0) → 70 m
3. Left to (0,0) → 70 m
4. Up to (0,70) → 70 m
But wait — that’s the full rectangle, but our shape is L-shaped, so the left side is not full 70 m — part is indented.

Correct outer path:
Start at top-left corner (0,70)
→ Right 70 m to (70,70)
→ Down 70 m to (70,0)
→ Left 70 m to (0,0)
→ Up 15 m to (0,15)
→ Right 40 m to (40,15)
→ Up 55 m to (40,70) — no, that’s not outer.

I think I’m overcomplicating. Use the “add all outer segments” method with given labels and inferred ones:

From diagram (standard worksheet L-shape):
- Top: 70 m
- Right side: 70 m
- Bottom: 70 m
- Left side has two parts: upper 15 m, then a horizontal 40 m to the right, then down 55 m — but the *outer* left side is only 15 m, then the step creates two more outer sides: the bottom of the step (40 m) and the left side of the lower part (55 m).

Actually, the perimeter is sum of all outer edges:
1. Top: 70
2. Right vertical: 70
3. Bottom: 70
4. Left vertical (lower part): 55
5. Horizontal step (inner bottom of top bar): 40
6. Left vertical (upper part): 15

Wait — no, edges 4,5,6 are *not* all outer. Let’s trace without crossing:

Start at top-left corner (A):
A → B (right 70)
B → C (down 70)
C → D (left 70)
D → E (up 55) ← this is along left side up to the step level
E → F (right 40) ← along the step top
F → A (up 15) ← back to start

So sides:
AB: 70
BC: 70
CD: 70
DE: 55
EF: 40
FA: 15

Sum = 70+70+70+55+40+15 = 280 m

✔ Check: Another way — perimeter of L-shape = perimeter of big rectangle (4×70=280) because the indent doesn’t change perimeter! Yes! For any orthogonal L-shape made by cutting a rectangle out of a corner, the perimeter stays the same as the original rectangle. Since outer dimensions are 70 m × 70 m, perimeter = 2×(70+70) = 280 m. ✔️

So:
- Area = 2700 m²
- Perimeter = 280 m

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Now compile all answers:

1. Rectangle:
Area = 340 in², Perimeter = 74 in

2. Triangle:
Area = 187.5 cm², Perimeter = 70 cm

3. Small L-shape (ft):
Area = 116 ft², Perimeter = 56 ft

4. Large L-shape (m):
Area = 2700 m², Perimeter = 280 m

Final Answer:
Area = 340 in², Perimeter = 74 in
Area = 187.5 cm², Perimeter = 70 cm
Area = 116 ft², Perimeter = 56 ft
Area = 2700 m², Perimeter = 280 m