Grade: Grade 6 Subject: Mathematics Unit: Geometry SAT: Geometry+Trigonometry ACT: Math

Word Problems: Geometry Applications

Apply your geometry knowledge to solve real-world problems involving area, perimeter, surface area, and volume.

Why Word Problems Matter

Geometry is Everywhere!

From building houses to wrapping gifts, from planning gardens to painting rooms - geometry helps us solve real problems every day.

Word problems are how math shows up in real life. Instead of being told "find the area of a rectangle with length 12 and width 8," you might need to figure out how much carpet to buy for your bedroom. The math is the same, but you need to identify what you are solving for!

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Home Improvement

Flooring, painting, fencing, landscaping

🎁
Packaging

Wrapping paper, boxes, shipping

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Outdoor Spaces

Gardens, pools, patios, sports fields

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Art & Design

Frames, canvases, layouts, patterns

Problem-Solving Strategy

The CUBES Method for Word Problems

C
Circle

Circle the numbers and units

U
Underline

Underline the question being asked

B
Box

Box key math words (area, perimeter, total)

E
Evaluate

Evaluate what steps to take

S
Solve

Solve and check your answer

Key Words to Watch For

  • Area keywords: cover, carpet, tile, paint, grass, floor space, surface
  • Perimeter keywords: fence, border, frame, edge, around, trim, outline
  • Surface area keywords: wrap, cover all sides, outside, total surface
  • Volume keywords: fill, hold, capacity, inside, storage space

Worked Examples

AREA Example 1: Carpeting a Room

Maria wants to carpet her rectangular bedroom. The room is 15 feet long and 12 feet wide. Carpet costs $4 per square foot. How much will it cost to carpet the entire room?
1
Identify what we need to find:
We need to find the total cost of carpet.
To find cost, we need: Area x Price per square foot
2
Find the area of the room:
Area = length x width = 15 x 12 = 180 sq ft
3
Calculate the total cost:
Cost = Area x Price = 180 x $4 = $720
Answer: It will cost $720 to carpet Maria's bedroom.

PERIMETER Example 2: Fencing a Garden

Mr. Johnson wants to put a fence around his rectangular vegetable garden to keep out rabbits. The garden is 18 meters long and 9 meters wide. Fencing costs $12 per meter. How much will it cost to fence the entire garden?
1
Identify what we need:
"Around" means perimeter!
Total cost = Perimeter x Price per meter
2
Find the perimeter:
P = 2l + 2w = 2(18) + 2(9) = 36 + 18 = 54 meters
3
Calculate the total cost:
Cost = 54 x $12 = $648
Answer: It will cost $648 to fence the garden.

COMPOSITE Example 3: Unusual Shaped Pool

A community pool has an L-shaped design. The main swimming area is 25 meters by 15 meters. A children's wading section extends from one corner, measuring 10 meters by 8 meters. What is the total water surface area of the pool?
25 m 15 m 10 m 8 m Main Kids
1
Break into two rectangles:
Main swimming area: 25 m x 15 m
Children's section: 10 m x 8 m
2
Calculate each area:
Main area: 25 x 15 = 375 m²
Children's area: 10 x 8 = 80 m²
3
Add the areas:
Total = 375 + 80 = 455 m²
Answer: The total water surface area is 455 square meters.

SURFACE AREA Example 4: Wrapping a Gift

Elena is wrapping a box-shaped gift that measures 30 cm long, 20 cm wide, and 10 cm tall. She wants to add 50 cm² extra for overlapping. How much wrapping paper does she need in total?
1
Identify the task:
"Wrapping" means we need surface area of the box.
Then add the extra for overlapping.
2
Calculate surface area:
SA = 2(lw) + 2(lh) + 2(wh)
SA = 2(30x20) + 2(30x10) + 2(20x10)
SA = 2(600) + 2(300) + 2(200)
SA = 1200 + 600 + 400 = 2200 cm²
3
Add extra for overlapping:
Total = 2200 + 50 = 2250 cm²
Answer: Elena needs 2,250 cm² (or 0.225 m²) of wrapping paper.
Pro Tip: Always re-read the problem after solving to make sure you answered what was asked. Did they want area or perimeter? Did they ask for a cost or just a measurement?

Practice Problems

Apply what you have learned to solve these word problems!

Problem 1: Painting a Wall

A rectangular wall is 14 feet wide and 9 feet tall. One gallon of paint covers 350 square feet. How much area needs to be painted?

Problem 2: Track Running

A rectangular track field is 100 meters long and 60 meters wide. Jasmine runs around the track 3 times. How far does she run in total?

Problem 3: Tiling a Bathroom

A bathroom floor is 8 feet by 6 feet. Each tile covers 1 square foot and costs $3. What is the total cost of tiles needed?

Problem 4: L-Shaped Deck

An L-shaped deck has a main section of 12 ft by 8 ft, and an extension of 6 ft by 5 ft. Wood planks cost $8 per square foot. What is the total cost for wood?

Problem 5: Triangular Banner

A triangular banner has a base of 4 feet and a height of 6 feet. Fabric costs $2 per square foot. How much does the fabric for the banner cost?

Problem 6: Gift Box

A gift box is 25 cm long, 15 cm wide, and 10 cm tall. What is the total surface area of the box?

Problem 7: Picture Frame

A rectangular picture is 24 inches by 18 inches. A frame 2 inches wide goes around the picture. What is the outer perimeter of the framed picture?

Problem 8: Soccer Field

A rectangular soccer field is 110 meters long and 75 meters wide. The groundskeeper needs to mow the entire field. How many square meters must be mowed?

Summary

Key Takeaways

  • Use the CUBES method to break down word problems systematically
  • Look for keywords to identify whether you need area, perimeter, or surface area
  • Draw a picture or diagram when helpful
  • Show all your work and include units in your answer
  • Always re-read to make sure you answered the actual question
  • Check if the problem asks for a measurement OR a cost/total
Common Mistake: Confusing area and perimeter! Remember: Area is the space INSIDE (measured in square units), while perimeter is the distance AROUND (measured in regular units).