Practice worksheet for calculating the area of composite figures, including rectangles, triangles, and irregular shapes.

Let's solve each of the composite figures step by step. The goal is to break each shape into simpler shapes (like rectangles, triangles, etc.), find their areas, and then add or subtract as needed.

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Problem 1

This figure can be split into two rectangles:

- Rectangle A: Top part: 2 in wide × 8 in high → Area = $ 2 \times 8 = 16 $ in²
- Rectangle B: Bottom part: 10 in wide × 7 in high → Area = $ 10 \times 7 = 70 $ in²

But wait — the top rectangle is only 2 inches wide, and the bottom is 10 inches wide. However, the total height on the left is 8 in, and on the right it's 7 in. So we can think of this as a large rectangle with a smaller one removed?

Actually, better approach: Split the shape into two rectangles:
- Left side: 2 in wide × 8 in tall → $ 2 \times 8 = 16 $
- Right side: 8 in wide (since total width is 10 in, minus 2 in) × 7 in tall → $ 8 \times 7 = 56 $

Wait — but the height of the right rectangle is only 7 in, while the left goes up to 8 in. So actually, the full base is 10 in, and the top has an "indent" of 2 in.

Better: Split vertically:
- Top rectangle: 2 in wide × 8 in high → $ 2 \times 8 = 16 $
- Bottom rectangle: (10 - 2) = 8 in wide × 7 in high → $ 8 \times 7 = 56 $

Total area = $ 16 + 56 = \boxed{72} $ in²

✔ Answer: 72 in²

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Problem 2

This is a "T-shaped" figure.

Break it into:
- Top rectangle: 30 in wide × 12 in high → $ 30 \times 12 = 360 $
- Middle rectangle: 10 in wide × 5 in high → $ 10 \times 5 = 50 $
- Bottom rectangle: But wait — there’s a gap. Actually, the figure has a central "notch".

Looking carefully:
- The full width is 30 in.
- There’s a central notch that is 10 in wide and 5 in deep.
- So instead of subtracting, let's break it into three rectangles:

#### Option: Divide into three parts
- Left rectangle: 12 in high × (30 - 10)/2 = 10 in wide? No — not symmetric.

Wait — look at the figure:

It's like a big rectangle with a small rectangle missing from the center bottom.

Actually, the top is 30 in wide × 12 in high → $ 30 \times 12 = 360 $

Then, below that, there are two side extensions, each 5 in high and 10 in wide? Wait, no.

From the diagram:
- The main body is 30 in wide × 12 in high → $ 30 \times 12 = 360 $
- Then, at the bottom, there's a recessed section of 10 in wide × 5 in deep → so we're subtracting a rectangle?

No — actually, the bottom has a "step" inward.

So the shape is:
- Top: 30 in × 12 in → $ 30 \times 12 = 360 $
- Then, below that, a central block of 10 in wide × 5 in high → $ 10 \times 5 = 50 $
- And two side blocks? No — it looks like the bottom is indented.

Wait — the figure shows:
- Total height: 12 in (top), then a notch of 5 in depth and 10 in width.

So the total area is:
- Large rectangle: 30 in × (12 + 5) = 30 × 17 = 510? But no — the bottom is only 5 in down.

Actually, the bottom has a gap of 10 in wide and 5 in deep.

So better: Think of it as a large rectangle minus a small rectangle.

But the shape isn't a full rectangle.

Alternative: Break into three rectangles:
1. Top rectangle: 30 in × 12 in → $ 30 \times 12 = 360 $
2. Left bottom rectangle: (30 - 10)/2 = 10 in wide × 5 in high → $ 10 \times 5 = 50 $
3. Right bottom rectangle: same → $ 10 \times 5 = 50 $

Wait — but the figure shows a central recess, so the bottom has two protrusions on the sides.

Yes — the total width is 30 in. The central notch is 10 in wide, so each side is (30 - 10)/2 = 10 in wide.

So:
- Top: 30 in × 12 in → $ 30 \times 12 = 360 $
- Left bottom: 10 in × 5 in → $ 50 $
- Right bottom: 10 in × 5 in → $ 50 $

Total area = $ 360 + 50 + 50 = \boxed{460} $ in²

✔ Answer: 460 in²

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Problem 3

This is a complex stepped shape.

We can break it into rectangles.

Label the parts from bottom up:

- Base rectangle: 70 in wide × 30 in high → $ 70 \times 30 = 2100 $
- Middle rectangle: 40 in wide × 10 in high → $ 40 \times 10 = 400 $
- Top rectangle: 30 in wide × 10 in high → $ 30 \times 10 = 300 $

Wait — let's check dimensions.

From the figure:
- Total height: 50 in
- Bottom layer: 30 in high
- Middle layer: 10 in high
- Top layer: 10 in high → total = 30+10+10=50 ✔️

Now widths:
- Bottom: 70 in wide
- Middle: 40 in wide (centered?)
- Top: 30 in wide

But the middle layer is offset — it's centered? From the drawing:
- Bottom: 70 in
- Middle: 40 in → so extends 15 in on each side? But the top is 30 in → so centered?

Let’s assume alignment.

So:
- Bottom rectangle: 70 × 30 = 2100
- Middle rectangle: 40 × 10 = 400
- Top rectangle: 30 × 10 = 300

Total area = $ 2100 + 400 + 300 = \boxed{2800} $ in²

✔ Answer: 2800 in²

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Problem 4

A house-like shape: triangle on top of a rectangle.

- Rectangle: 24 in wide × 10 in high → $ 24 \times 10 = 240 $
- Triangle: base = 24 in, height = 9 in → area = $ \frac{1}{2} \times 24 \times 9 = 12 \times 9 = 108 $

Total area = $ 240 + 108 = \boxed{348} $ in²

✔ Answer: 348 in²

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Problem 5

An L-shaped figure with a corner cut out.

We can break it into:
- Big rectangle: 28 in wide × 12 in high → $ 28 \times 12 = 336 $
- Cut-out rectangle: 4 in wide × 12 in high? No — the cut is only 4 in deep and 22 in wide?

Wait — the figure shows:
- A rectangle of 28 in × 12 in
- But a corner is cut off: 4 in deep and 22 in wide? No — the cut is only 4 in wide and 22 in long?

Wait — from the diagram:
- The top is 28 in
- The bottom is shorter — there's a cutout on the lower left
- The cutout is 4 in deep and 22 in wide? That doesn’t make sense.

Wait — the figure shows:
- Main rectangle: 28 in wide × 12 in high
- But a right triangle or rectangle is missing?

Actually, it's a rectangle with a small rectangle cut out from the bottom-left.

The cutout is 4 in high and 22 in wide? No — the label says “22 in” along the bottom, and “4 in” vertical.

Wait — the figure has:
- Top: 28 in
- Bottom: a segment of 22 in, then a cutout of 4 in depth

So the shape is:
- A large rectangle of 28 in × 12 in → $ 28 \times 12 = 336 $
- Minus a small rectangle of 4 in × (28 - 22)? No.

Wait — the cutout is only 4 in high and 22 in wide? That would be huge.

Wait — the horizontal segment is labeled 22 in, and the vertical drop is 4 in.

So the missing part is a rectangle of:
- Width: 28 - 22 = 6 in?
- Height: 4 in?

No — the figure shows the bottom is 22 in, and the cutout is 4 in deep.

So the main rectangle is 28 in × 12 in → 336

But from the bottom-left, a rectangle of 6 in wide × 4 in high is missing?

Wait — no. The figure shows:
- The bottom edge is 22 in long
- The left side drops down 4 in
- So the cutout is a rectangle of 6 in wide × 4 in high?

Wait — if the total width is 28 in, and the bottom is only 22 in, then the overhang on the left is 6 in? But the drop is 4 in.

So the shape is:
- A rectangle of 28 in × 12 in
- Minus a small rectangle of 6 in × 4 in? No — that’s not correct.

Better: Break into two rectangles.

Option:
1. Top rectangle: 28 in × (12 - 4) = 28 × 8 = 224
2. Bottom rectangle: 22 in × 4 in = 88

Total area = $ 224 + 88 = \boxed{312} $ in²

✔ Answer: 312 in²

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Problem 6

A trapezoid-like shape with a step.

Break into:
- Rectangle on the right: 22 in wide × 40 in high → $ 22 \times 40 = 880 $
- Trapezoid or triangle on the left?

Wait — the left side has a step.

From the figure:
- Total base: 50 in
- The right part is 22 in wide
- So the left part is 50 - 22 = 28 in wide
- But the height changes: from 18 in to 40 in

Wait — the left side is a right triangle?

Look:
- The vertical leg is 20 in (from 18 to 40? 40 - 18 = 22? But labeled 20 in)

Wait — the figure shows:
- Vertical drop: 20 in (labeled)
- Horizontal base: 18 in (labeled)
- Then a rectangle of 22 in × 40 in

So the shape is:
- Triangle on the left: base = 18 in, height = 20 in → area = $ \frac{1}{2} \times 18 \times 20 = 180 $
- Rectangle on the right: 22 in × 40 in → $ 22 \times 40 = 880 $

But wait — the total base is 50 in, and 18 + 22 = 40 in? Not enough.

Wait — the base is 50 in. The triangle has base 18 in, and the rectangle has width 22 in → total 40 in? Missing 10 in.

Wait — perhaps the rectangle is 22 in wide, and the triangle is 18 in wide, but they’re adjacent?

Wait — the total base is 50 in. The rectangle is 22 in wide, so the remaining 28 in must be the triangle base?

But the triangle is labeled with base 18 in and height 20 in.

Wait — maybe the left part is a trapezoid?

Let’s re-analyze.

From the figure:
- The right part is a rectangle: 22 in wide × 40 in high → $ 22 \times 40 = 880 $
- The left part is a trapezoid or polygon with:
- Base: 50 - 22 = 28 in
- But the height is only 18 in? No — the vertical drop is 20 in.

Wait — the figure shows:
- The height of the left side is 18 in (horizontal line)
- The vertical rise is 20 in (dashed line)
- The base of the triangle is 18 in

So the left part is a right triangle with:
- Base = 18 in
- Height = 20 in → area = $ \frac{1}{2} \times 18 \times 20 = 180 $

But what about the rest?

Wait — the total base is 50 in. The triangle has base 18 in, so the remaining base is 32 in? But the rectangle is 22 in wide → inconsistency.

Wait — perhaps the rectangle is 22 in wide, and the triangle is 18 in wide, but they are not aligned.

Wait — the total base is 50 in. The rectangle is 22 in wide, so the left part must be 50 - 22 = 28 in wide.

But the triangle is labeled with base 18 in — that can’t be.

Wait — the triangle is not the entire left part.

Wait — the figure shows:
- A step: from ground level, go up 18 in horizontally, then up 20 in vertically to reach 40 in.
- So the left side is a right triangle with:
- Horizontal leg = 18 in
- Vertical leg = 20 in
- Then a rectangle to the right: 22 in wide × 40 in high

But the base of the triangle is 18 in, and the rectangle is 22 in wide → total base = 18 + 22 = 40 in, but the total base is 50 in → missing 10 in.

Ah! So the bottom has a horizontal segment of 18 in, then a vertical rise of 20 in, then a horizontal segment of 22 in, then a vertical down to 40 in.

Wait — the total base is 50 in.

So:
- From left: horizontal 18 in
- Then vertical 20 in
- Then horizontal 22 in
- Then vertical down to 40 in

But the total horizontal length is 18 + 22 = 40 in → but base is 50 in → missing 10 in.

Wait — perhaps the rectangle is 22 in wide, but the triangle is 18 in wide, and there's a gap?

No — the figure shows the bottom is continuous.

Wait — the bottom is 50 in long.

The triangle has base 18 in, and the rectangle has base 22 in → total 40 in → still missing 10 in.

Wait — perhaps the rectangle is not 22 in wide — the 22 in is the vertical dimension?

No — the label says “22 in” next to the top of the rectangle.

Wait — the figure shows:
- The right side is a rectangle: 22 in wide × 40 in high → yes
- The left side is a trapezoid or polygon with:
- Bottom base: 50 - 22 = 28 in
- Top base: 18 in (horizontal segment)
- Height: 20 in (vertical rise)

So the left part is a trapezoid:
- Two parallel sides: 28 in (bottom) and 18 in (top)
- Height = 20 in

Area = $ \frac{1}{2} \times (28 + 18) \times 20 = \frac{1}{2} \times 46 \times 20 = 460 $

Then the rectangle on the right: 22 in × 40 in = 880

Total area = $ 460 + 880 = \boxed{1340} $ in²

✔ Answer: 1340 in²

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✔ Final Answers:

1) 72 in²
2) 460 in²
3) 2800 in²
4) 348 in²
5) 312 in²
6) 1340 in²

Let me know if you'd like a visual breakdown for any of them!