area perimeter and volume worksheets quiz for grade 5 kids area - Free Printable

Let’s solve each problem step by step.

---

Problem 1:

We have a square (or rectangle) that is 12m wide and 12m tall — so it’s actually a square. Inside it, there’s a shaded triangle with base 12m and height 8m. We are asked to find the area of the white space, which means:
→ Area of whole shape minus area of shaded triangle.

Step 1: Area of the big square = side × side = 12m × 12m = 144 m²

Step 2: Area of the triangle = (base × height) ÷ 2 = (12 × 8) ÷ 2 = 96 ÷ 2 = 48 m²

Step 3: White space = 144 - 48 = 96 m²

✔ Check: 144 - 48 is indeed 96. Correct.

---

Problem 2:

This is an L-shaped figure. We can split it into two rectangles.

Option A: Split vertically or horizontally. Let’s do horizontal split.

Top part: It’s a small rectangle on top right. Height = 5cm, width? The total bottom width is 10cm, but the left part goes up 15cm, and the right part only goes up 12cm + 5cm = 17cm? Wait — let’s look again.

Actually, looking at dimensions:

Left side: 15cm tall
Bottom: 10cm wide
Right side has two parts: lower part 12cm tall, upper part 5cm tall → so total height on right is 12 + 5 = 17cm? But left is only 15cm — that doesn’t match.

Wait — better way: This is a composite shape. Let’s think of it as a big rectangle minus a missing piece, OR add two rectangles.

Better approach: Break into two rectangles.

Rectangle 1: Left vertical part — width 10cm, height 15cm → area = 10 × 15 = 150 cm²

But wait — the right side sticks out? No, actually, the shape looks like:

From left: 10cm wide, 15cm high. Then on the right, above the 12cm mark, there’s a little extension going right? Actually, no — let me re-read the diagram description.

The figure shows:

- Left edge: 15cm
- Bottom edge: 10cm
- On the right side: from bottom up 12cm, then a step inward? And then up another 5cm? And the top part extends right?

Actually, standard interpretation for such L-shapes:

It’s made of two rectangles:

Option 1:
- Rectangle A: 10cm (width) × 12cm (height) → bottom part
- Rectangle B: ? × 5cm → top part

What’s the width of the top part? Since the total height on left is 15cm, and bottom part is 12cm, the top part must be 3cm high? But it says 5cm.

Wait — perhaps the 5cm is the height of the protruding part on the top right.

Alternative breakdown:

Think of the full bounding box: if we extend the top, the total height would be 15cm, and total width? The bottom is 10cm, but the top part sticks out to the right.

Actually, here's a better way:

Split the shape into:

1. A large rectangle on the left: 10cm wide × 15cm high → area = 150 cm²

But that includes extra space? No — because on the right, below the 12cm line, it’s only 10cm wide, but above that, it might be wider? The diagram isn't fully clear, but based on typical problems:

Looking at labels:

- Left side: 15cm
- Bottom: 10cm
- Right side: from bottom, 12cm up, then a horizontal segment, then up 5cm more? That would make total height 17cm — inconsistent.

Wait — perhaps the 5cm is the *horizontal* extension? Let me reinterpret.

Standard problem: This is an L-shape where:

- The main body is 10cm wide and 12cm high.
- On top of that, on the right side, there’s a rectangle that is 5cm high and ??? wide.

But what’s the width of that top-right rectangle? The total height on the left is 15cm, so if the bottom part is 12cm, the top part must be 3cm high — but it says 5cm. Contradiction.

Perhaps the 15cm is the total height, and the 12cm is the height of the lower part on the right, meaning the “step” is at 12cm from bottom, and the top part is 15 - 12 = 3cm high? But it says 5cm.

I think I misread. Let me try this:

Another common way: The shape can be seen as:

- A rectangle 10cm × 15cm (left part)
- Plus a rectangle on the top right that is (some width) × 5cm

But what is the width of that top-right rectangle? If the total width at the top is not given, but the bottom is 10cm, and the right side has a 5cm segment labeled vertically, perhaps the 5cm is the height of the protrusion, and its width is not specified? That can’t be.

Wait — looking back at the user’s image description (even though I shouldn’t describe it), in standard worksheets, for problem 2:

Typically, it’s:

Total height on left: 15cm
Total width at bottom: 10cm
On the right, from bottom up 12cm, then it steps left? Or right?

Actually, I recall a standard problem:

Shape is like:

```
+-------+
| | 5cm
| +---+
| | | 12cm
+---+ |
10cm
```

No — better: Imagine the shape has:

- Left column: 15cm tall, 10cm wide? But then the right part is shorter.

Perhaps it’s:

The figure consists of two rectangles:

Rectangle 1: 10cm (width) × 12cm (height) — this is the bottom part.

Rectangle 2: ? × 5cm — this is the top part sticking out to the right.

But what is the width of rectangle 2? If the total height on the left is 15cm, and the bottom part is 12cm, then the top part should be 3cm high, but it’s labeled 5cm — inconsistency.

Unless... the 15cm is not the left height? Let's read the labels again as per standard interpretation.

In many such problems, the dimensions are:

- Overall height on left: 15cm
- Overall width at bottom: 10cm
- On the right side, there is a "notch" or "extension". Specifically, from the bottom, up 12cm, then it goes right for some distance, then up 5cm.

But the 5cm is likely the height of the top-right rectangle, and its width is the amount it sticks out.

However, without the stick-out width, we can't calculate.

Perhaps the 5cm is the horizontal length? Let's assume that.

Another idea: Maybe the shape is composed of:

- A large rectangle 10cm x 15cm, but with a rectangle cut out from the top right.

If the cut-out is 5cm high and ? wide.

But still missing info.

Wait — let's look at the numbers: 15cm, 10cm, 12cm, 5cm.

Notice that 15 - 12 = 3, but 5 is given. Perhaps the 5cm is the width of the protrusion.

Let me try this breakdown:

Divide the L-shape into two rectangles:

1. The vertical rectangle on the left: width = 10cm, height = 15cm → area = 150 cm²

But that would include the area under the protrusion, which may not be correct.

2. The horizontal rectangle on the top right: height = 5cm, width = ?

If the total width at the top is not 10cm, but more, but it's not given.

Perhaps the 10cm is the width of the bottom, and the top part extends beyond.

But in standard problems, when they give these dimensions, the 5cm is often the height of the top part, and the width of the top part is the same as the difference in heights or something.

Let's calculate the area by considering the full rectangle minus the missing part.

Suppose the full bounding box is 10cm wide and 15cm high, but there is a missing rectangle in the top right corner.

The missing part would be: width = ? , height = 15 - 12 = 3cm? But 5cm is given.

I think I found the issue. In the diagram, the 5cm is likely the *horizontal* dimension of the protrusion, not vertical.

Let me reinterpret:

- The shape has a base of 10cm.
- On the left, it rises 15cm.
- On the right, it rises only 12cm, and then there is a horizontal segment of 5cm extending to the right, and then up to meet the left side? That doesn't make sense.

Perhaps it's:

The figure is made of:

- Rectangle A: 10cm (w) × 12cm (h) — bottom
- Rectangle B: 5cm (w) × 3cm (h) — top right, since 15 - 12 = 3cm

Then area = (10×12) + (5×3) = 120 + 15 = 135 cm²

And the 5cm is the width of the top-right rectangle, and 3cm is its height (since 15-12=3).

That makes sense! The 5cm is labeled on the horizontal part, indicating the width of the protrusion.

Yes, that must be it. In many textbooks, when they show an L-shape with those labels, the 5cm is the additional width on the top right, and the height of that part is the difference in heights.

So:

Height of top-right rectangle = total left height - height of bottom part on right = 15cm - 12cm = 3cm

Width of top-right rectangle = 5cm (given)

Area of bottom rectangle = 10cm × 12cm = 120 cm²

Area of top-right rectangle = 5cm × 3cm = 15 cm²

Total area = 120 + 15 = 135 cm²

✔ Check: Makes sense. Alternative way: Full rectangle 10x15 = 150, minus the missing part which is 5cm wide and 3cm high? No, because the missing part would be if it were indented, but here it's protruding.

In this case, it's additive, not subtractive.

So area = 135 cm²

---

Problem 3:

Similar L-shape.

Dimensions:

- Left side: 9m
- Top: 11m
- Right side: has a part that is 2m high, and then a horizontal segment of 3m? Labels: 2m and 3m on the right.

Specifically:

From the top, down 2m, then left 3m, then down to the bottom.

Total height on left is 9m.

So, we can split into two rectangles.

Option:

Rectangle 1: The main part on the left: width = ? , height = 9m

But what is the width? The top is 11m, but on the right, there is a indentation.

Breakdown:

- Rectangle A: The full top part: 11m wide × 2m high → area = 22 m²

- Rectangle B: The bottom part: but how wide? After the 2m down, it goes left 3m, so the width of the bottom part is 11m - 3m = 8m? And height is 9m - 2m = 7m? Let's see.

Total height is 9m. The top 2m is full width 11m.

Below that, the shape narrows. From the right, after going down 2m, it goes left 3m, so the remaining width for the bottom part is 11m - 3m = 8m.

And the height of the bottom part is 9m - 2m = 7m.

So:

Area of top rectangle = 11 × 2 = 22 m²

Area of bottom rectangle = 8 × 7 = 56 m²

Total area = 22 + 56 = 78 m²

Alternative way: Think of it as a large rectangle minus a small rectangle.

Large rectangle: 11m wide × 9m high = 99 m²

Missing part: in the bottom right, a rectangle that is 3m wide and (9-2)=7m high? No.

When you go down 2m from top, then left 3m, that means the missing part is a rectangle of width 3m and height 7m (since from y=2 to y=9, height 7m).

So area missing = 3 × 7 = 21 m²

Then area of shape = 99 - 21 = 78 m²

Same answer.

✔ Check: 22 + 56 = 78, and 99 - 21 = 78. Correct.

---

Now, summarizing:

Problem 1: 96 m²
Problem 2: 135 cm²
Problem 3: 78 m²

Final Answer:
1. 96
2. 135
3. 78