Scale Drawings & Proportional Geometry Quiz

1) A rectangular garden measures 12 m by 18 m. On a drawing with scale 1 cm = 3 m, what are the garden's dimensions?

4 cm × 6 cm

6 cm × 9 cm

12 cm × 18 cm

3 cm × 5 cm

Garden dimensions

Scale: 1 cm = 3 m. Garden is 12 m by 18 m.

So, 12 ÷ 3 = 4 and 18 ÷ 3 = 6.

The drawing shows 4 cm × 6 cm.

Explanation

Garden dimensions

Scale: 1 cm = 3 m. Garden is 12 m by 18 m.

So, 12 ÷ 3 = 4 and 18 ÷ 3 = 6.

The drawing shows 4 cm × 6 cm.

2) The scale of a map is 1:250 (1 cm = 250 m). How many kilometers does 8 cm represent?

1.5 km

2 km

2.5 km

3 km

Map distance

Scale: 1 cm = 250 m. The map shows 8 cm.

So, 8 × 250 = 2000 = 2 km.

The actual distance is 2 kilometers.

Explanation

Map distance

Scale: 1 cm = 250 m. The map shows 8 cm.

So, 8 × 250 = 2000 = 2 km.

The actual distance is 2 kilometers.

3) A model of a rectangular box has dimensions 2 cm m 3 cm m 4 cm. The scale is 1:10 (1 cm = 10 m). What is the volume of the actual box?

2,000 m³

12,000 m³

24,000 m³

48,000 m³

Box volume

Scale: 1 cm = 10 m. Drawing = 2 × 3 × 4 cm → actual = 20 × 30 × 40 m.

Volume = 20 × 30 × 40 = 24,000.

The actual volume is 24,000 m³.

Explanation

Box volume

Scale: 1 cm = 10 m. Drawing = 2 × 3 × 4 cm → actual = 20 × 30 × 40 m.

Volume = 20 × 30 × 40 = 24,000.

The actual volume is 24,000 m³.

4) On a scale drawing, a roof has a base of 5 cm and a height of 3 cm. The scale is 1 cm = 2 m. What is the actual area of the roof base?

18 m²

30 m²

42 m²

56 m²

Roof base area

Scale: 1 cm = 2 m. Drawing base = 5 cm → 10 m. Height = 3 cm → 6 m.

Area = ½ × 10 × 6 = 30.

The actual area is 30 m².

Explanation

Roof base area

Scale: 1 cm = 2 m. Drawing base = 5 cm → 10 m. Height = 3 cm → 6 m.

Area = ½ × 10 × 6 = 30.

The actual area is 30 m².

5) A rectangle is drawn on a map with a scale of 1 cm = 5 m. If the rectangle is 3 cm long, what is the actual length?

8 m

10 m

15 m

20 m

Rectangle length on a map.

Scale: 1 cm = 5 m. The rectangle is 3 cm long.

So, 3 × 5 = 15.

The actual length is 15 meters.

Explanation

Rectangle length on a map.

Scale: 1 cm = 5 m. The rectangle is 3 cm long.

So, 3 × 5 = 15.

The actual length is 15 meters.

6) On a blueprint, 2 cm represents 4 m. How many meters does 7 cm represent?

12 m

14 m

28 m

35 m

Blueprint length

Scale: 2 cm = 4 m. So, 1 cm = 2 m. The line is 7 cm.

So, 7 × 2 = 14.

The actual length is 14 meters.

Explanation

Blueprint length

Scale: 2 cm = 4 m. So, 1 cm = 2 m. The line is 7 cm.

So, 7 × 2 = 14.

The actual length is 14 meters.

7) The scale on a map is 1 inch = 12 miles. If two towns are 3.5 inches apart on the map, what is their actual distance?

24 miles

36 miles

42 miles

48 miles

Distance between towns

Scale: 1 in = 12 miles. The map shows 3.5 in.

So, 3.5 × 12 = 42.

The actual distance is 42 miles.

Explanation

Distance between towns

Scale: 1 in = 12 miles. The map shows 3.5 in.

So, 3.5 × 12 = 42.

The actual distance is 42 miles.

8) A model car is built at a scale of 1:20. If the model's length is 10 cm, what is the actual car's length?

150 cm

180 cm

200 cm

220 cm

Model car length

Scale: 1:20 means the real car is 20 times bigger.

So, 10 × 20 = 200.

The actual length is 200 cm.

Explanation

Model car length

Scale: 1:20 means the real car is 20 times bigger.

So, 10 × 20 = 200.

The actual length is 200 cm.

9) A triangle on a scale drawing has sides of 4 cm, 6 cm, and 8 cm. If the scale is 1 cm = 2 ft, what is the perimeter of the actual triangle?

30 ft

36 ft

40 ft

44 ft

Triangle perimeter

Scale: 1 cm = 2 ft. Sides: 4 cm = 8 ft, 6 cm = 12 ft, 8 cm = 16 ft.

Perimeter = 8 + 12 + 16 = 36.

The actual perimeter is 36 feet.

Explanation

Triangle perimeter

Scale: 1 cm = 2 ft. Sides: 4 cm = 8 ft, 6 cm = 12 ft, 8 cm = 16 ft.

Perimeter = 8 + 12 + 16 = 36.

The actual perimeter is 36 feet.

10) A map has a scale of 1 cm = 50 km. If the actual distance between two cities is 250 km, how far apart should they be on the map?

3 cm

4 cm

5 cm

6 cm

Distance on map

Scale: 1 cm = 50 km. Actual distance = 250 km.

So, 250 ÷ 50 = 5.

The map distance is 5 cm.

Explanation

Distance on map

Scale: 1 cm = 50 km. Actual distance = 250 km.

So, 250 ÷ 50 = 5.

The map distance is 5 cm.

11) The scale on a drawing is 1 in = 8 ft. If a wall is 12 in on the drawing, how long is the actual wall?

72 ft

84 ft

90 ft

96 ft

Wall length

Scale: 1 in = 8 ft. The drawing shows 12 in.

So, 12 × 8 = 96.

The actual wall length is 96 feet.

Explanation

Wall length

Scale: 1 in = 8 ft. The drawing shows 12 in.

So, 12 × 8 = 96.

The actual wall length is 96 feet.

12) A scale model of a building is constructed at 1:100. The height of the model is 1.8 m. What is the actual building's height?

180 m

200 m

220 m

250 m

Building height

Scale: 1:100 means the real building is 100 times bigger.

So, 1.8 × 100 = 180.

The actual height is 180 meters.

Explanation

Building height

Scale: 1:100 means the real building is 100 times bigger.

So, 1.8 × 100 = 180.

The actual height is 180 meters.

13) On a scale drawing, a park is represented as a square with side length 5 cm. The scale is 1 cm = 20 m. What is the actual area of the park?

1,000 m²

4,000 m²

10,000 m²

20,000 m²

Park area

Scale: 1 cm = 20 m. Side of the square = 5 × 20 = 100 m.

Area = 100 × 100 = 10,000.

The actual area is 10,000 m².

Explanation

Park area

Scale: 1 cm = 20 m. Side of the square = 5 × 20 = 100 m.

Area = 100 × 100 = 10,000.

The actual area is 10,000 m².

14) A model train set is built at 1:5 scale (1 cm = 5 m). If the actual train is 25 m long, what is the model length?

2.5 cm

3 cm

4.5 cm

5 cm

Train length

Scale: 1 cm = 5 m. Actual train = 25 m.

So, 25 ÷ 5 = 5.

The model length is 5 cm.

Explanation

Train length

Scale: 1 cm = 5 m. Actual train = 25 m.

So, 25 ÷ 5 = 5.

The model length is 5 cm.

15) A football field is 100 m long. On a scale drawing with 1 cm = 10 m, how long is the field on the drawing?

5 cm

8 cm

10 cm

12 cm

Football field length

Scale: 1 cm = 10 m. Actual field = 100 m.

So, 100 ÷ 10 = 10.

The drawing length is 10 cm.

Explanation

Football field length

Scale: 1 cm = 10 m. Actual field = 100 m.

So, 100 ÷ 10 = 10.

The drawing length is 10 cm.

16) A floor plan uses the scale 1 in = 3 ft. If a window is 2 in wide on the plan, what is its actual width?

4 ft

5 ft

6 ft

8 ft

Window width

Scale: 1 in = 3 ft. The drawing shows 2 in.

So, 2 × 3 = 6.

The actual width is 6 feet.

Explanation

Window width

Scale: 1 in = 3 ft. The drawing shows 2 in.

So, 2 × 3 = 6.

The actual width is 6 feet.

17) A drawing of a rectangular pool shows dimensions of 6 cm by 4 cm. The scale is 1 cm = 2 m. What is the pool's actual perimeter?

20 m

28 m

36 m

40 m

Pool perimeter

Scale: 1 cm = 2 m. Drawing = 6 cm by 4 cm → actual = 12 m by 8 m.

Perimeter = 2(12 + 8) = 40.

The actual perimeter is 40 meters.

Explanation

Pool perimeter

Scale: 1 cm = 2 m. Drawing = 6 cm by 4 cm → actual = 12 m by 8 m.

Perimeter = 2(12 + 8) = 40.

The actual perimeter is 40 meters.

18) If two lines intersecThe scale on a city map is 1 in = 5 miles. If two locations are 4.6 inches apart, how many miles is that?t, how many pairs of vertical angles are formed?

20 miles

22 miles

23 miles

24 miles

City map distance

Scale: 1 in = 5 miles. The drawing shows 4.6 in.

So, 4.6 × 5 = 23.

The actual distance is 23 miles.

Explanation

City map distance

Scale: 1 in = 5 miles. The drawing shows 4.6 in.

So, 4.6 × 5 = 23.

The actual distance is 23 miles.

19) A museum floor plan shows a rectangular hall as 8 cm by 12 cm. The scale is 1 cm = 4 m. What is the actual area of the hall?

1536 m²

2056 m²

3184 m²

5012 m²

Hall area

Scale: 1 cm = 4 m. Drawing = 8 × 12 cm → actual = 32 × 48 m.

Area = 32 × 48 = 1536.

The actual area is 1536 m².

Explanation

Hall area

Scale: 1 cm = 4 m. Drawing = 8 × 12 cm → actual = 32 × 48 m.

Area = 32 × 48 = 1536.

The actual area is 1536 m².

20) A model airplane is built to a scale of 1:4 (1 cm = 4 m). The wingspan of the model is 25 cm. What is the actual wingspan?

80 m

90 m

100 m

120 m

Airplane wingspan

Scale: 1 cm = 4 m. Model wingspan = 25 cm.

So, 25 × 4 = 100.

The actual wingspan is 100 meters.

Explanation

Airplane wingspan

Scale: 1 cm = 4 m. Model wingspan = 25 cm.

So, 25 × 4 = 100.

The actual wingspan is 100 meters.