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Unit 4 Advanced Worksheet

Geometry & Measurement Challenges

Challenge yourself with complex geometry and measurement problems including multi-step calculations and real-world applications.

Question 1: A rectangular garden is 15 m long and 8 m wide. You want to put a fence around it and plant grass inside. Find BOTH the perimeter (for fencing) AND area (for grass).

Answer: Perimeter: 46 m, Area: 120 m²

Steps:

  1. Perimeter = 2(15 + 8) = 2(23) = 46 m
  2. Area = 15 × 8 = 120 m²
  3. Need 46 m of fence and 120 m² of grass seed

Question 2: Two angles are supplementary. One angle is 125°. Find the other angle.

Answer: 55°

Steps:

  1. Supplementary angles add to 180°
  2. 180° - 125° = 55°
  3. Answer: 55°

Question 3: A storage box is 20 in long, 12 in wide, and 8 in tall. What is its volume? If you stack two identical boxes, what's the total volume?

Answer: One box: 1,920 in³, Two boxes: 3,840 in³

Steps:

  1. Volume of one box = 20 × 12 × 8 = 1,920 in³
  2. Two boxes = 1,920 × 2 = 3,840 in³
  3. Answer: 1,920 in³ and 3,840 in³

Question 4: A rectangular room is 6 m × 4 m × 3 m tall. Find the volume AND the area of floor space.

Answer: Volume: 72 m³, Floor area: 24 m²

Steps:

  1. Volume = 6 × 4 × 3 = 72 m³
  2. Floor area = 6 × 4 = 24 m²
  3. Answer: 72 m³ and 24 m²

Question 5: Convert 5 yards to inches. (Hint: yards → feet → inches)

Answer: 180 inches

Steps:

  1. 5 yards × 3 feet/yard = 15 feet
  2. 15 feet × 12 inches/foot = 180 inches
  3. Answer: 180 inches

Question 6: A square has perimeter 48 cm. Find its area.

Answer: 144 cm²

Steps:

  1. Side = 48 ÷ 4 = 12 cm
  2. Area = 12 × 12 = 144 cm²
  3. Answer: 144 cm²

Question 7: A picture frame is 18 in × 14 in. How much frame material needed (perimeter)? What wall area does it cover (area)?

Answer: Perimeter: 64 in, Area: 252 in²

Steps:

  1. Perimeter = 2(18 + 14) = 2(32) = 64 in
  2. Area = 18 × 14 = 252 in²
  3. Answer: 64 in and 252 in²

Question 8: An aquarium is 50 cm × 25 cm × 30 cm. How many liters of water can it hold? (1 liter = 1,000 cm³)

Answer: 37.5 liters

Steps:

  1. Volume = 50 × 25 × 30 = 37,500 cm³
  2. Liters = 37,500 ÷ 1,000 = 37.5
  3. Answer: 37.5 liters

Question 9: Three angles in a triangle add to 180°. Two angles are 45° and 60°. Find the third angle.

Answer: 75°

Steps:

  1. Sum = 180°
  2. 45° + 60° + ? = 180°
  3. 105° + ? = 180°
  4. ? = 75°

Question 10: A rectangular field is 80 m × 50 m. How many laps around the field equals 1 kilometer?

Answer: About 3.85 laps (or 4 laps rounded)

Steps:

  1. Perimeter = 2(80 + 50) = 260 m per lap
  2. 1 km = 1,000 m
  3. Laps = 1,000 ÷ 260 ≈ 3.85 laps

Question 11: Two rectangles have area 36 cm². Rectangle A is 9×4. Rectangle B is 6×6. Which has smaller perimeter?

Answer: Rectangle B (6×6, perimeter 24)

Steps:

  1. Rectangle A: P = 2(9+4) = 26 cm
  2. Rectangle B: P = 2(6+6) = 24 cm
  3. Square-ish shape has smaller perimeter!

Question 12: Convert 96 ounces to pounds.

Answer: 6 pounds

Steps:

  1. 16 ounces = 1 pound
  2. 96 ÷ 16 = 6
  3. Answer: 6 pounds

Question 13: A cube has volume 125 cm³. Find the length of one edge AND the total surface area of all 6 faces.

Answer: Edge: 5 cm, Surface area: 150 cm²

Steps:

  1. Edge³ = 125, so edge = 5 cm
  2. One face = 5×5 = 25 cm²
  3. 6 faces = 25×6 = 150 cm²

Question 14: A swimming pool is 25 m long, 10 m wide, and 2 m deep. How many cubic meters of water? Convert to liters. (1 m³ = 1,000 liters)

Answer: 500 m³ = 500,000 liters

Steps:

  1. Volume = 25 × 10 × 2 = 500 m³
  2. Liters = 500 × 1,000 = 500,000 L
  3. That's a LOT of water!

Question 15: Convert 3 miles to feet. (1 mile = 5,280 feet)

Answer: 15,840 feet

Steps:

  1. 3 miles × 5,280 feet/mile
  2. 15,840 feet
  3. Answer: 15,840 feet

Question 16: A box has volume 240 cm³ and base area 40 cm². A second identical box is stacked on top. What's the total height?

Answer: 12 cm

Steps:

  1. Height of one box = 240 ÷ 40 = 6 cm
  2. Two boxes stacked = 6 + 6 = 12 cm
  3. Answer: 12 cm total height

Question 17: A triangle has angles 30°, 70°, and ?. Find the missing angle.

Answer: 80°

Steps:

  1. Triangle angles sum to 180°
  2. 30° + 70° + ? = 180°
  3. 100° + ? = 180°
  4. ? = 80°

Question 18: Convert 4 gallons to cups. (1 gallon = 16 cups)

Answer: 64 cups

Steps:

  1. 4 gallons × 16 cups/gallon
  2. 64 cups
  3. Answer: 64 cups

Question 19: A rectangular prism is 12 cm × 8 cm × 5 cm. Find volume AND the total edge length if there are 12 edges (4 of each dimension).

Answer: Volume: 480 cm³, Total edge: 100 cm

Steps:

  1. Volume = 12 × 8 × 5 = 480 cm³
  2. Edges: 4(12) + 4(8) + 4(5) = 48+32+20 = 100 cm
  3. Answer: 480 cm³ and 100 cm

Question 20: You need to paint a room's walls. Room is 5 m × 4 m × 3 m tall. Find floor area (for carpet) AND wall area (for painting, 4 walls only).

Answer: Floor: 20 m², Walls: 54 m²

Steps:

  1. Floor = 5 × 4 = 20 m²
  2. Two walls: 2(5×3) = 30 m²
  3. Other two walls: 2(4×3) = 24 m²
  4. Total walls: 30+24 = 54 m²

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