Scale Drawings and Proportional Geometry Quiz

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| Questions: 20 | Updated: Nov 20, 2025
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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?

Explanation

Garden scale

Scale: 1 cm = 3 m.

12 ÷ 3 = 4 cm; 18 ÷ 3 = 6 cm.

The garden drawing is 4 cm × 6 cm.

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About This Quiz
Scale Drawings And Proportional Geometry Quiz - Quiz

Are you ready to see how math connects to real life? Take this quiz we’ve prepared for you where you’ll use scale drawings to solve problems where small models represent much bigger things. You’ll work with examples like roads, beams, ropes, and sports fields — just like real situations you... see moresee every day. By practicing proportions, you’ll learn how to calculate actual lengths, distances, and areas with confidence. Get ready to discover how geometry helps explain the world around you!
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2) 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?

Explanation

Box volume

Scale: 1 cm = 10 m → actual: 20×30×40.

20 × 30 × 40 = 24,000.

The box volume is 24,000 m³.

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

Explanation

Map distance

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

8 × 250 = 2000 m = 2 km.

The distance is 2 km.

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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?

Explanation

Roof area

Scale: 1 cm = 2 m → base 10 m, height 6 m.

Area = ½ × 10 × 6 = 30.

The roof area is 30 m².

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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?

Explanation

Map length

Scale: 1 cm = 5 m. The line is 3 cm.

So, 3 × 5 = 15.

The actual length is 15 meters.

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

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.

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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?

Explanation

Map distance

Scale: 1 in = 12 mi. The distance is 3.5 in.

So, 3.5 × 12 = 42.

The actual distance is 42 miles.

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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?

Explanation

Model length

Scale: 1:20. The model is 10 cm long.

So, 10 × 20 = 200.

The actual car’s length is 200 cm.

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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?

Explanation

Triangle sides

Each cm = 2 ft. Sides are 4, 6, 8 cm.

So, 8 + 12 + 16 = 36.

The actual perimeter is 36 ft.

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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?

Explanation

Map scale

Scale: 1 cm = 50 km. The real distance is 250 km.

So, 250 ÷ 50 = 5.

They are 5 cm apart on the map.

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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?

Explanation

Drawing scale

Scale: 1 in = 8 ft. The wall is 12 in.

So, 12 × 8 = 96.

The actual wall is 96 ft long.

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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?

Explanation

Model height

Scale: 1:100. Model is 1.8 m tall.

So, 1.8 × 100 = 180.

The actual building is 180 m high.

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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?

Explanation

Park area

Scale: 1 cm = 20 m. Each side = 5 cm → 100 m.

Area = 100 × 100 = 10,000.

The actual area is 10,000 m².

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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?

Explanation

Train model

Scale: 1 cm = 5 m.

25 ÷ 5 = 5.

The model is 5 cm long.

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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?

Explanation

Field length

Scale: 1 cm = 10 m.

100 ÷ 10 = 10.

The drawing shows 10 cm.

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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?

Explanation

Blueprint width

Scale: 1 in = 3 ft. The window is 2 in.

So, 2 × 3 = 6.

The window is 6 ft wide.

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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?

Explanation

Pool size

Scale: 1 cm = 2 m.

6→12 m, 4→8 m.

Perimeter = 2(12 + 8) = 40.

The pool’s perimeter is 40 m.

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18) The 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?

Explanation

Map distance

Scale: 1 in = 5 mi.

4.6 × 5 = 23.

The distance is 23 miles.

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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?

Explanation

Hall area

Scale: 1 cm = 4 m → actual 32 × 48 m.

Area = 32 × 48 = 1536.

The hall area is 1536 m².

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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?

Explanation

Airplane wingspan

Scale: 1 cm = 4 m.

25 × 4 = 100.

The wingspan is 100 m.

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A rectangular garden measures 12 m by 18 m. On a drawing with scale 1...
A model of a rectangular box has dimensions 2 cm m 3 cm m 4 cm. The...
The scale of a map is 1:250 (1 cm = 250 m). How many kilometers does 8...
On a scale drawing, a roof has a base of 5 cm and a height of 3 cm....
A rectangle is drawn on a map with a scale of 1 cm = 5 m. If the...
On a blueprint, 2 cm represents 4 m. How many meters does 7 cm...
The scale on a map is 1 inch = 12 miles. If two towns are 3.5 inches...
A model car is built at a scale of 1:20. If the model's length is 10...
A triangle on a scale drawing has sides of 4 cm, 6 cm, and 8 cm. If...
A map has a scale of 1 cm = 50 km. If the actual distance between two...
The scale on a drawing is 1 in = 8 ft. If a wall is 12 in on the...
A scale model of a building is constructed at 1:100. The height of the...
On a scale drawing, a park is represented as a square with side length...
A model train set is built at 1:5 scale (1 cm = 5 m). If the actual...
A football field is 100 m long. On a scale drawing with 1 cm = 10 m,...
A floor plan uses the scale 1 in = 3 ft. If a window is 2 in wide on...
A drawing of a rectangular pool shows dimensions of 6 cm by 4 cm. The...
The scale on a city map is 1 in = 5 miles. If two locations are 4.6...
A museum floor plan shows a rectangular hall as 8 cm by 12 cm. The...
A model airplane is built to a scale of 1:4 (1 cm = 4 m). The wingspan...
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