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

Guided Practice: Geometry Foundations

Work through geometry problems step-by-step with hints and immediate feedback to build your confidence.

How to Use This Guided Practice

Practice Makes Perfect

This lesson provides scaffolded practice problems where you can see worked examples, get hints when stuck, and check your answers as you go.

Tips for Success

  • Try first - Attempt each problem before looking at hints
  • Show your work - Write out each step, even on scratch paper
  • Learn from mistakes - If you get one wrong, study the solution carefully
  • Track your progress - Use the progress tracker at the bottom

Quick Reference: Key Formulas

Rectangle Area
A = l x w
Triangle Area
A = 1/2 x b x h
Rectangle Perimeter
P = 2l + 2w
Triangle Perimeter
P = a + b + c

Part 1: Area Calculations

Guided Problem 1: Rectangle Area

A rectangular garden has a length of 12 meters and a width of 8 meters. What is the area of the garden?
1
Identify the formula:
For a rectangle, Area = length x width
A = l x w
2
Identify the values:
Length (l) = 12 m
Width (w) = 8 m
3
Substitute and calculate:
A = 12 x 8 = 96 m²
Answer: The area of the garden is 96 square meters.
Your Turn!

A rectangular parking lot is 45 meters long and 20 meters wide. What is the area?

m²
Hint: Use A = l x w. Multiply 45 x 20.

Guided Problem 2: Triangle Area

A triangular sail has a base of 6 feet and a height of 10 feet. What is the area of the sail?
1
Identify the formula:
For a triangle, Area = 1/2 x base x height
A = 1/2 x b x h
2
Identify the values:
Base (b) = 6 ft
Height (h) = 10 ft
3
Substitute and calculate:
A = 1/2 x 6 x 10 = 1/2 x 60 = 30 ft²
Answer: The area of the sail is 30 square feet.
Your Turn!

A triangular garden bed has a base of 14 meters and a height of 8 meters. What is the area?

m²
Hint: Use A = 1/2 x b x h. Calculate 1/2 x 14 x 8.

Part 2: Perimeter Calculations

Guided Problem 3: Rectangle Perimeter

A picture frame is 16 inches long and 12 inches wide. How much framing material is needed to go around the entire picture?
1
Identify what we are finding:
The distance around the picture = Perimeter
P = 2l + 2w (or P = 2(l + w))
2
Identify the values:
Length (l) = 16 inches
Width (w) = 12 inches
3
Substitute and calculate:
P = 2(16) + 2(12) = 32 + 24 = 56 inches
Answer: 56 inches of framing material is needed.
Your Turn!

A rectangular pool is 25 meters long and 10 meters wide. What is the perimeter of the pool?

m
Hint: P = 2l + 2w = 2(25) + 2(10). Add the results.

Guided Problem 4: Triangle Perimeter

A triangular sign has sides measuring 5 cm, 7 cm, and 9 cm. What is the perimeter of the sign?
1
Identify the formula:
For a triangle, Perimeter = sum of all sides
P = a + b + c
2
Identify the values:
Side a = 5 cm, Side b = 7 cm, Side c = 9 cm
3
Add all sides:
P = 5 + 7 + 9 = 21 cm
Answer: The perimeter of the sign is 21 cm.
Your Turn!

A triangular garden has sides of 8 m, 11 m, and 15 m. What is the perimeter?

m
Hint: Add all three sides: 8 + 11 + 15.

Part 3: Composite Figures

Guided Problem 5: L-Shaped Figure Area

Find the area of an L-shaped room where the main section is 10 m by 6 m, and a smaller section extends 4 m by 3 m.
10 m 6 m 4 m 3 m
1
Break into two rectangles:
Rectangle 1 (top): 10 m x 6 m
Rectangle 2 (left extension): 4 m x (total height - 6 m)
Note: We need to figure out the extension height = 3 m (given as 4 m x 3 m)
2
Calculate each area:
Rectangle 1: A = 10 x 6 = 60 m²
Rectangle 2: A = 4 x 3 = 12 m²
3
Add the areas:
Total Area = 60 + 12 = 72 m²
Answer: The area of the L-shaped room is 72 square meters.
Your Turn!

An L-shaped patio has a main section of 8 m by 5 m, with an extension of 3 m by 4 m. What is the total area?

m²
Hint: Main section: 8 x 5 = 40 m². Extension: 3 x 4 = 12 m². Add them together.

Guided Problem 6: Rectangle with Cutout

A rectangular board is 20 cm by 15 cm. A square hole of 4 cm x 4 cm is cut from the center. What is the remaining area?
1
Find the area of the full rectangle:
Full area = 20 x 15 = 300 cm²
2
Find the area of the cutout:
Cutout area = 4 x 4 = 16 cm²
3
Subtract the cutout from the full area:
Remaining area = 300 - 16 = 284 cm²
Answer: The remaining area is 284 square centimeters.
Your Turn!

A rectangular sign is 30 cm by 24 cm. A circular viewing hole requires cutting out a square of 6 cm x 6 cm. What is the remaining area?

cm²
Hint: Full area: 30 x 24 = 720 cm². Cutout: 6 x 6 = 36 cm². Subtract: 720 - 36.

Part 4: Independent Practice

Try these problems on your own! Select the correct answer.

Problem 7

What is the area of a rectangle with length 18 cm and width 7 cm?

Problem 8

What is the perimeter of a square with side length 9 m?

Problem 9

What is the area of a triangle with base 16 in and height 9 in?

Problem 10

A rectangle is 12 ft by 8 ft with a 2 ft x 2 ft square cut out. What is the remaining area?

Your Progress

Problems Completed

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Key Takeaways

  • Always identify the correct formula before starting
  • Label your dimensions clearly (length, width, base, height)
  • For composite figures, break into simpler shapes first
  • Include units in your final answer (cm², m², ft², etc.)
  • Double-check your arithmetic, especially with multi-step problems