This worksheet features six math problems focused on scale drawings of geometric figures, including calculating distances, perimeters, and areas using scale factors. It includes visual examples such as a treasure map, a wooden box, a house floor plan, a triangle pyramid, a cake, and a map distance.

Let’s solve each problem one by one, step by step. We’ll check our work carefully before giving the final answer.

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Problem 1:

Logan made a treasure hunt map. The treasure is 25 cm away from his location on the map.
Scale: 1 cm = 5 meters.

So, to find real distance:
25 cm × 5 meters/cm = 125 meters

✔ Check: 25 × 5 = 125 → correct.

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Problem 2:

Jordan has a square box with all sides = 6 cm.
He increases each side by 1.6 cm → new side = 6 + 1.6 = 7.6 cm

Perimeter of square = 4 × side → 4 × 7.6 = 30.4 cm

Area of square = side × side → 7.6 × 7.6

Let’s calculate that:

7.6 × 7.6
= (7 + 0.6) × (7 + 0.6)
= 7×7 + 7×0.6 + 0.6×7 + 0.6×0.6
= 49 + 4.2 + 4.2 + 0.36
= 49 + 8.4 + 0.36 = 57.76 cm²

✔ Check: 7.6 × 7.6 = 57.76 → correct.

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Problem 3:

Abigail’s house scale drawing:
Each 6 cm on drawing = 12 ft in real life.

So, scale factor: 6 cm → 12 ft → so 1 cm = 2 ft.

Now look at the drawing dimensions:

- Top and bottom: 10 cm → real length = 10 × 2 = 20 ft
- Left and right: 9 cm → real width = 9 × 2 = 18 ft
- There’s also a 7 cm line inside — probably height of something? But question asks for “actual dimensions of Abigail’s house” — likely meaning outer rectangle: 10 cm by 9 cm → so 20 ft by 18 ft.

Wait — the diagram shows:

Top: 10 cm
Sides: 9 cm
Bottom: 8 cm? Wait — let me re-read.

Actually, looking at the description: it says “a scale drawing of her house can be seen below” and lists:

“10cm” on top, “9cm” on left, “7cm” vertical inside, “9cm” on right, “8cm” on bottom.

Hmm — this might be an L-shaped or irregular shape? But since it's labeled as a house, and we’re asked for “dimensions”, maybe they mean overall length and width?

But note: top is 10 cm, bottom is 8 cm — that suggests it’s not a rectangle. However, the left and right are both 9 cm — so perhaps it’s a rectangle with a notch? Or maybe it’s a typo?

Wait — actually, looking again: the figure is drawn as a rectangle with a small rectangle cut out? But the labels say:

Left side: 9 cm
Right side: 9 cm
Top: 10 cm
Bottom: 8 cm
And a vertical line inside labeled 7 cm — which might be the height of the inner part?

This is confusing. But perhaps the intended interpretation is that the house is represented by the outer rectangle: 10 cm wide and 9 cm tall? But then why is bottom 8 cm?

Alternatively — maybe the 8 cm is the base of the main part, and the 10 cm includes an extension? Without seeing the actual image, we have to go by text.

But wait — the problem says: “what are the actual dimensions of Abigail’s house?”

Given that, and common worksheet problems, it’s likely that the house is meant to be a rectangle with length 10 cm and width 9 cm — and the 8 cm and 7 cm are internal features not needed for overall dimensions.

But let’s think differently: if the drawing has top = 10 cm, bottom = 8 cm, and sides = 9 cm, it might be a trapezoid? But that seems unlikely for a house.

Another possibility: the 10 cm is total width, 9 cm is total height, and the 8 cm and 7 cm are parts of rooms — but the question asks for “dimensions of the house”, so probably overall.

I think safest assumption: the house is 10 cm long and 9 cm wide on the drawing.

Scale: 6 cm = 12 ft → so 1 cm = 2 ft.

Thus:

Length: 10 cm × 2 = 20 ft
Width: 9 cm × 2 = 18 ft

But wait — the bottom is labeled 8 cm. Maybe the house is not rectangular? Perhaps it’s composed of two rectangles?

Looking at typical such problems, sometimes the figure is like a rectangle with a smaller rectangle attached or removed.

But since no clear diagram, and the problem says “scale drawing of her house”, and gives multiple measurements, perhaps we need to interpret the outer boundaries.

Assume the maximum width is 10 cm (top), maximum height is 9 cm (sides). So overall dimensions: 10 cm by 9 cm.

Convert using scale: 1 cm = 2 ft → 20 ft by 18 ft.

But let’s double-check the scale: “each 6 cm on the scale drawing equals 12 ft” → so ratio is 6:12 = 1:2 → yes, 1 cm = 2 ft.

So I’ll go with 20 ft by 18 ft.

However, another thought: maybe the 8 cm is the actual floor length, and 10 cm includes walls or something? Unlikely.

Perhaps the house is L-shaped, and we need to give overall length and width.

In many worksheets, when they show a shape with those labels, the overall bounding box is 10 cm wide and 9 cm tall.

So I’ll proceed with that.

Final answer for #3: 20 feet by 18 feet

But let’s see if there’s another way. Suppose the 7 cm is the height of a section, and 9 cm is total height — then maybe the house has a porch or something. But without more info, I think 20 ft x 18 ft is reasonable.

Wait — perhaps the 8 cm is the base, and 10 cm is the top, making it a trapezoid? Then area would be different, but question asks for “dimensions”, plural, so likely length and width.

I think we should take the largest horizontal and vertical measures: 10 cm and 9 cm.

So: 10 cm → 20 ft, 9 cm → 18 ft.

✔ Confirmed.

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Problem 4:

Olivia saw a triangle pyramid model. She enlarged it with scale factor 1.2.

Original triangle: base 8 cm, two equal sides 6 cm each, height 7 cm (dashed line).

First, perimeter of original triangle: 6 + 6 + 8 = 20 cm

After scaling by 1.2: new perimeter = 20 × 1.2 = 24 cm

Area of original triangle: (base × height)/2 = (8 × 7)/2 = 56/2 = 28 cm²

When you scale a 2D shape by factor k, area scales by k².

So new area = 28 × (1.2)² = 28 × 1.44

Calculate 28 × 1.44:

28 × 1 = 28
28 × 0.4 = 11.2
28 × 0.04 = 1.12
Total: 28 + 11.2 = 39.2; +1.12 = 40.32 cm²

✔ Check: 1.2² = 1.44; 28 × 1.44 = let's compute: 20×1.44=28.8, 8×1.44=11.52, total 28.8+11.52=40.32 → correct.

Note: The problem says “triangle shaped pyramid” — but then gives a 2D triangle with base and height. Probably means the triangular face, and we’re to find perimeter and area of that face after scaling. Since it’s a pyramid, but only one triangle is given, I think we treat it as a 2D triangle for this problem.

So perimeter: 24 cm, area: 40.32 cm²

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Problem 5:

Carter’s cake: rectangular, length 8 cm, width 6 cm.

Mom adds 1 cm of cream around the cake — meaning, she adds a border of 1 cm on all sides.

So, new length = original length + 1 cm on left + 1 cm on right = 8 + 2 = 10 cm

New width = 6 + 1 + 1 = 8 cm

Perimeter of new rectangle = 2 × (length + width) = 2 × (10 + 8) = 2 × 18 = 36 cm

Area = length × width = 10 × 8 = 80 cm²

✔ Check: adding 1 cm border increases each dimension by 2 cm → yes.

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Problem 6:

Max makes scale drawing: distance between Salt Lake City and Arizona is 21 cm on drawing.

Scale: each 7 cm = 250 kilometers.

So, how many times does 7 cm fit into 21 cm? 21 ÷ 7 = 3

So real distance = 3 × 250 km = 750 kilometers

✔ Check: 21 / 7 = 3; 3 × 250 = 750 → correct.

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Now, compiling all answers:

1. 125 meters
2. Perimeter: 30.4 cm, Area: 57.76 cm²
3. 20 feet by 18 feet
4. Perimeter: 24 cm, Area: 40.32 cm²
5. Perimeter: 36 cm, Area: 80 cm²
6. 750 kilometers

But for problem 3, I’m still a bit unsure about the dimensions. Let me reconsider.

In problem 3, the drawing has:

- Top: 10 cm
- Bottom: 8 cm
- Left: 9 cm
- Right: 9 cm
- Internal vertical: 7 cm

This looks like a rectangle with a smaller rectangle cut out from the bottom or top? For example, maybe the house is 10 cm wide at top, but only 8 cm wide at bottom, and 9 cm tall, with a 7 cm high section.

But typically, in such problems, if it's a house, and they ask for "dimensions", they might mean the overall length and width.

Perhaps the 10 cm is the full width, 9 cm is full height, and the 8 cm and 7 cm are for internal rooms, not affecting overall size.

Maybe the figure is a rectangle 10 cm by 9 cm, and the 8 cm and 7 cm are red herrings or for another purpose.

Another idea: perhaps the house is composed of two rectangles: one 10 cm by 7 cm, and another 8 cm by 2 cm or something. But that complicates it.

Given that the problem says "scale drawing of her house" and then gives those measurements, and asks for "actual dimensions", I think the intended answer is based on the outermost points.

So width: max of 10 cm and 8 cm → 10 cm
Height: 9 cm

So 10 cm × 9 cm → scaled to 20 ft × 18 ft.

I think that's fine.

Some might argue that since bottom is 8 cm, the width varies, but for simplicity, we'll go with 20 ft by 18 ft.

Final Answers:

1. 125 meters
2. Perimeter: 30.4 cm, Area: 57.76 cm²
3. 20 feet by 18 feet
4. Perimeter: 24 cm, Area: 40.32 cm²
5. Perimeter: 36 cm, Area: 80 cm²
6. 750 kilometers

Now, to present them clearly.

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Final Answer:
1. 125 meters
2. Perimeter: 30.4 cm, Area: 57.76 cm²
3. 20 feet by 18 feet
4. Perimeter: 24 cm, Area: 40.32 cm²
5. Perimeter: 36 cm, Area: 80 cm²
6. 750 kilometers