2D shapes and perimeter
Advanced Area & Perimeter Worksheet: Geometry Formulas and Real-World Application Problems (Grades 6-9)
Part 1: Area Calculations and Formula Mastery (Units are squared)
1. Rectangle: A living room floor measures 8 meters long and 5 meters wide. What is the total area of the floor?
Formula Used: ____________________
2. Square: A piece of paper has sides that are 30 centimeters each. Calculate the area of the paper.
Formula Used: ____________________
3. Triangle: A sail for a boat has a base of 10 feet and a height of 15 feet. What is the area of the sail?
Formula Used: ____________________
4. Parallelogram: A paved courtyard is shaped like a parallelogram with a base of 20 feet and a perpendicular height of 12 feet. Find the area.
Formula Used: ____________________
5. Circle: A circular rug has a radius of 2 meters. What is the area of the rug? (Use $\pi \approx 3.14$)
Formula Used: ____________________
6. Rectangle: A swimming pool cover is 12 feet wide and 9 feet long. What is the total area of the cover?
Formula Used: ____________________
7. Square: Find the area of a square garden plot with sides measuring 15 cm.
Formula Used: ____________________
8. Triangle: Calculate the area of a triangular sign with a base of 6 meters and a height of 4 meters.
Formula Used: ____________________
9. Parallelogram: An advertising banner shaped like a parallelogram has a base of 15 inches and a height of 8 inches. What is its area?
Formula Used: ____________________
10. Circle: A circular pond has a radius of 5 kilometers. Find the area of the pond. (Use $\pi \approx 3.14$)
Formula Used: ____________________
Part 2: Perimeter and Circumference Calculations (Essential Geometry Practice)
11. Rectangle: A rectangular picture frame is 35 cm long and 20 cm wide. What is the perimeter of the frame?
Formula Used: ____________________
12. Compound Shape: Find the perimeter of a shape with six sides measuring 4 cm, 6 cm, 2 cm, 3 cm, 2 cm, and 9 cm.
Formula Used: ____________________
13. Circle: A bicycle wheel has a diameter of 60 cm. What is the circumference of the wheel? (Use $\pi \approx 3.14$)
Formula Used: ____________________
14. Rectangle: A garden plot is 10 meters long and 4 meters wide. How much netting is needed to go around the garden?
Formula Used: ____________________
15. Square: A square sandbox has sides measuring 18 feet. Find the perimeter of the sandbox.
Formula Used: ____________________
16. Triangle: A triangular piece of wood has side lengths of 5 inches, 7 inches, and 10 inches. What is the perimeter?
Formula Used: ____________________
17. Parallelogram: A parallelogram-shaped sign has adjacent sides of 12 meters and 8 meters. Calculate its perimeter.
Formula Used: ____________________
18. Compound Shape: The perimeter of an irregular hexagon has sides measuring 5 cm, 5 cm, 2 cm, 3 cm, 3 cm, and 8 cm. What is the total perimeter?
Formula Used: ____________________
19. Circle: Calculate the circumference of a circular track with a radius of 7 meters. (Use $\pi \approx 3.14$)
Formula Used: ____________________
20. Equilateral Triangle: An equilateral triangle has a side length of 9 mm. What is its perimeter?
Formula Used: ____________________
Part 3: Advanced Geometry & Real-World Spatial Reasoning
21. Trapezoid (Trapezium) Area: A flower bed is shaped like a trapezoid with parallel bases measuring 10 feet and 14 feet. The height of the trapezoid is 5 feet. What is the area of the flower bed?
Formula Used: ____________________
22. Rhombus Area: A kite (shaped like a rhombus) has diagonals measuring 40 cm and 30 cm. Calculate the area of the kite.
Formula Used: ____________________
23. Trapezoid (Trapezium) Area: Find the area of a trapezoid with bases of 8 meters and 6 meters, and a height of 4 meters.
Formula Used: ____________________
24. Rhombus Area: A diamond-shaped window is a rhombus with diagonals measuring 10 inches and 15 inches. Find the area of the window?
Formula Used: ____________________
25. Combined Problem (Square): A gardener is tending a square vegetable patch with sides of 9 feet.
- a) What is the total area of the patch (for seed calculation)?
- b) What is the perimeter of the patch (for fencing calculation)?
Formula Used: ____________________
26. Combined Problem (Rectangle): A bulletin board is 7 meters long and 3 meters wide.
- a) Find the area of the bulletin board.
- b) Find the perimeter of the bulletin board.
Formula Used: ____________________
27. Circle Application: A circular dining table has a diameter of 1 meter. If you walk around the table once, what distance have you traveled? (Find the Circumference using $\pi \approx 3.14$)
Formula Used: ____________________
28. Area Application: A painter needs to cover a rectangular wall that is 4 meters wide and 3 meters tall. What is the total area the painter must cover?
Formula Used: ____________________
29. Perimeter Application: A contractor needs to fence a triangular plot of land with sides measuring 10m, 12m, and 14m. How much total fencing material is required?
Formula Used: ____________________
30. Compound Area Application: A floor space is made up of a 5-unit by 5-unit square attached next to a 5-unit by 4-unit rectangle. What is the total area of the floor space?
Formula Used: ____________________
Answer Key
- Rectangle Area: $8 \text{m} \times 5 \text{m} = 40 \text{m}^2$.
- Square Area: $30 \text{cm} \times 30 \text{cm} = 900 \text{cm}^2$.
- Triangle Area: $\frac{1}{2} \times 10 \text{ft} \times 15 \text{ft} = 75 \text{ft}^2$.
- Parallelogram Area: $20 \text{ft} \times 12 \text{ft} = 240 \text{ft}^2$.
- Circle Area: $3.14 \times (2 \text{m})^2 = 12.56 \text{m}^2$.
- Rectangle Area: $12 \text{ft} \times 9 \text{ft} = 108 \text{ft}^2$.
- Square Area: $15 \text{cm} \times 15 \text{cm} = 225 \text{cm}^2$.
- Triangle Area: $\frac{1}{2} \times 6 \text{m} \times 4 \text{m} = 12 \text{m}^2$.
- Parallelogram Area: $15 \text{in} \times 8 \text{in} = 120 \text{in}^2$.
- Circle Area: $3.14 \times (5 \text{km})^2 = 78.5 \text{km}^2$.
- Rectangle Perimeter: $2(35 \text{cm} + 20 \text{cm}) = 110 \text{cm}$.
- Compound Perimeter: $4 + 6 + 2 + 3 + 2 + 9 = 26 \text{cm}$.
- Circle Circumference: $3.14 \times 60 \text{cm} = 188.4 \text{cm}$.
- Rectangle Perimeter: $2(10 \text{m} + 4 \text{m}) = 28 \text{m}$.
- Square Perimeter: $4 \times 18 \text{ft} = 72 \text{ft}$.
- Triangle Perimeter: $5 \text{in} + 7 \text{in} + 10 \text{in} = 22 \text{in}$.
- Parallelogram Perimeter: $2(12 \text{m} + 8 \text{m}) = 40 \text{m}$.
- Compound Perimeter: $5 + 5 + 2 + 3 + 3 + 8 = 26 \text{cm}$.
- Circle Circumference: $2 \times 3.14 \times 7 \text{m} = 43.96 \text{m}$.
- Equilateral Triangle Perimeter: $3 \times 9 \text{mm} = 27 \text{mm}$.
- Trapezoid Area: $\frac{1}{2}(10 \text{ft} + 14 \text{ft}) \times 5 \text{ft} = 60 \text{ft}^2$.
- Rhombus Area: $\frac{1}{2}(40 \text{cm} \times 30 \text{cm}) = 600 \text{cm}^2$.
- Trapezoid Area: $\frac{1}{2}(8 \text{m} + 6 \text{m}) \times 4 \text{m} = 28 \text{m}^2$.
- Rhombus Area: $\frac{1}{2}(10 \text{in} \times 15 \text{in}) = 75 \text{in}^2$.
- Combined Problem (Square): (a) Area: $9 \times 9 = 81 \text{ft}^2$. (b) Perimeter: $4 \times 9 = 36 \text{ft}$.
- Combined Problem (Rectangle): (a) Area: $7 \times 3 = 21 \text{m}^2$. (b) Perimeter: $2(7+3) = 20 \text{m}$.
- Circle Application (Circumference): $3.14 \times 1 \text{m} = 3.14 \text{m}$.
- Area Application (Rectangle): $4 \text{m} \times 3 \text{m} = 12 \text{m}^2$.
- Perimeter Application (Triangle): $10 \text{m} + 12 \text{m} + 14 \text{m} = 36 \text{m}$.
- Compound Area Application: $(5 \times 5) + (5 \times 4) = 25 + 20 = 45 \text{units}^2$.
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