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Math Word Problems quiz

Geometry Word Problems Quiz

Practice 10 geometry word problems involving area, volume, similarity, scale drawings, dimensions, composite figures, trapezoids, the Pythagorean theorem, surface area, and measurement. Use hints when needed and review the explanation after each answer.

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1 Question 1 of 10
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A rectangular garden is 18 meters long and 12 meters wide. A walkway 1.5 meters wide is built all the way around the outside of the garden. What is the area of the walkway?

Hint: Add the walkway width to both sides of each dimension, find the outer rectangle area, then subtract the garden area.
Explanation: The outer dimensions are 18 + 3 = 21 meters and 12 + 3 = 15 meters. Outer area = 21 × 15 = 315 m². Garden area = 18 × 12 = 216 m². Walkway area = 315 - 216 = 99 m².
2 Question 2 of 10
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A cylindrical water tank has radius 2.5 meters and height 6 meters. It is filled to 80% of its capacity. Using π = 3.14, how many cubic meters of water are in the tank?

Hint: Find the full cylinder volume with V = πr²h, then take 80% of that volume.
Explanation: Full volume = 3.14 × 2.5² × 6 = 3.14 × 6.25 × 6 = 117.75 m³. At 80% full, water volume = 117.75 × 0.80 = 94.2 m³.
3 Question 3 of 10
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A 1.8-meter-tall person casts a 2.4-meter shadow. At the same time, a tree casts a 10-meter shadow. Assuming the sun creates similar triangles, how tall is the tree?

Hint: Set up equal height-to-shadow ratios for the person and the tree.
Explanation: The ratios are proportional: 1.8/2.4 = h/10. Since 1.8 ÷ 2.4 = 0.75, h = 0.75 × 10 = 7.5 meters.
4 Question 4 of 10
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A rectangular room measures 7.2 cm by 4.8 cm on a scale drawing. The scale is 1 cm = 2.5 meters. What is the actual area of the room?

Hint: Convert each drawing dimension to its real length before finding area.
Explanation: Actual length = 7.2 × 2.5 = 18 meters. Actual width = 4.8 × 2.5 = 12 meters. Area = 18 × 12 = 216 m².
5 Question 5 of 10
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A rectangle has perimeter 74 meters. Its length is 7 meters greater than its width. What is the area of the rectangle?

Hint: Let the width be w and the length be w + 7. Use 2l + 2w = 74.
Explanation: Let width = w and length = w + 7. Then 2w + 2(w + 7) = 74, so 4w + 14 = 74 and w = 15. The length is 22. Area = 15 × 22 = 330 m².
6 Question 6 of 10
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An L-shaped floor can be viewed as a 14 m by 10 m rectangle with a 5 m by 4 m rectangular corner removed. If 10% extra tile is ordered for cutting and waste, how many square meters of tile should be ordered?

Hint: Find the L-shaped area first, then multiply that area by 1.10.
Explanation: Large rectangle area = 14 × 10 = 140 m². Removed corner = 5 × 4 = 20 m². Floor area = 120 m². Adding 10% for waste gives 120 × 1.10 = 132 m².
7 Question 7 of 10
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A trapezoidal field has parallel sides 28 meters and 42 meters long. The perpendicular distance between them is 18 meters. What is the area of the field?

Hint: Use A = 1/2(b₁ + b₂)h.
Explanation: Area = 1/2 × (28 + 42) × 18 = 1/2 × 70 × 18 = 35 × 18 = 630 m².
8 Question 8 of 10
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A 6.5-meter ladder leans against a vertical wall. The foot of the ladder is 2.5 meters from the wall. How high up the wall does the ladder reach?

Hint: The ladder is the hypotenuse of a right triangle. Use the Pythagorean theorem.
Explanation: Let the height be h. Then h² + 2.5² = 6.5². So h² = 42.25 - 6.25 = 36, giving h = 6 meters.
9 Question 9 of 10
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An open-top rectangular storage box is 8 cm long, 5 cm wide, and 3 cm high. How much material is needed to make the box, not including any overlap or waste?

Hint: Because the box has no top, include the base and four side faces only.
Explanation: Base area = 8 × 5 = 40 cm². Two long sides total 2 × (8 × 3) = 48 cm². Two short sides total 2 × (5 × 3) = 30 cm². Total material = 40 + 48 + 30 = 118 cm².
10 Question 10 of 10
Not answered

A rectangular tank is 2.4 meters long, 1.5 meters wide, and 1.2 meters high. It is filled to 75% of its capacity. How many liters of water does it contain?

Hint: Find the tank volume in cubic meters, take 75%, then use 1 m³ = 1,000 liters.
Explanation: Full volume = 2.4 × 1.5 × 1.2 = 4.32 m³. At 75% full, water volume = 4.32 × 0.75 = 3.24 m³. Since 1 m³ = 1,000 L, the tank contains 3,240 liters.

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Geometry modeling studio

Geometry word problems begin before the formula: first decide what shape the situation creates

These 10 problems use walkways, tanks, shadows, scale drawings, unknown dimensions, composite floors, trapezoids, ladders, open-top boxes, and liquid capacity. The important skill is translating words into a diagram with dimensions, units, and constraints.

AreaComposite figuresVolumeSimilarity ScaleDimensionsPythagorean theoremSurface area
Outer-minus-inner area

A walkway around a garden is not found by adding 1.5 meters to only one side

Because the walkway surrounds the garden, each overall dimension grows by twice the walkway width.

Outer length: 18 + 1.5 + 1.5 = 21 m
Outer width: 12 + 1.5 + 1.5 = 15 m
Walkway area: 21×15 − 18×12 = 99 m²
Similar-triangle shadow model

Equal sun angles create proportional height-to-shadow ratios

A person and a tree cast shadows at the same time, so their right triangles are similar.

1.8 / 2.4 = tree height / 10 → tree height = 7.5 m
Scale drawing

Scale lengths first; then calculate the real area

A common mistake is to multiply the drawing area by the length scale only once. Area changes in two dimensions.

7.2 cm → 18 m
4.8 cm → 12 m
Actual area = 18 × 12 = 216 m²
Composite geometry

Complex-looking shapes become simpler when you add or subtract familiar pieces

L-shaped floor

Start with the large rectangle, subtract the missing corner, then add the 10% tile allowance.

Trapezoidal field

Average the two parallel sides, then multiply by the perpendicular height.
Measurement in three dimensions

Volume, surface area, and capacity answer different questions about the same object

The last problems force you to identify whether the situation asks for space inside, material covering faces, or liquid after a fill percentage.

Cylinder volumecapacity before applying fill level
Open-top surface areabase + four sides, but no lid
Tank capacityvolume × fill fraction, then convert units
After the quiz

Review the modeling step that failed, not just the final arithmetic

Geometry errors often begin with the wrong diagram, missing dimension, face, scale factor, or unit conversion.

Area modelswalkways, trapezoids, composite regions
Similarity & scaleshadows, drawings, proportional dimensions
Right trianglesunknown height or distance from a diagonal
3D measurementvolume, capacity, surface material, liters
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