Perimeters and Areas of Plane Shapes – Basic 6 Mathematics Lesson Note (Second Term)

Regular Shapes – Formulas and Properties

Rectangle

Properties:

• 4 sides, opposite sides equal
• 4 right angles (90°)
• Opposite sides parallel

Formulas:

• Perimeter = 2(length + width)
• Area = length × width

Square

Properties:

• 4 equal sides
• 4 right angles (90°)
• All sides parallel to opposite sides

Formulas:

• Perimeter = 4 × side
• Area = side × side = side²

Triangle

Properties:

• 3 sides, 3 angles
• Sum of angles = 180°

Formulas:

• Perimeter = side 1 + side 2 + side 3
• Area = ½ × base × height

Parallelogram

Properties:

• Opposite sides equal and parallel
• Opposite angles equal
• Adjacent angles add up to 180°

Formulas:

• Perimeter = 2(length + width)
• Area = base × height

Trapezium

Properties:

• One pair of parallel sides
• Non-parallel sides may be equal or unequal

Formulas:

• Perimeter = sum of all four sides
• Area = ½ × (sum of parallel sides) × height

Circle

Properties:

• All points on edge are equal distance from center
• No corners or sides

Formulas:

• Perimeter (Circumference) = 2πr or πd
• Area = πr²
• π ≈ 3.14 or 22/7

Exercise A – Regular Shape Properties

Match each shape with its properties:

1. Rectangle – ________________
2. Square – ________________
3. Circle – ________________
4. Parallelogram – ________________

Properties to choose from:

• All points equal distance from center
• 4 equal sides, 4 right angles
• Opposite sides equal and parallel, 4 right angles
• Opposite sides equal and parallel, opposite angles equal

Exercise B – Perimeter Calculations

Find the perimeter of these shapes:

1. Rectangle: length = 8 cm, width = 5 cm Perimeter: ______ cm
2. Square: side = 7 cm Perimeter: ______ cm
3. Triangle: sides = 6 cm, 8 cm, 10 cm Perimeter: ______ cm
4. Circle: radius = 14 cm (use π = 22/7) Perimeter: ______ cm
5. Parallelogram: length = 12 cm, width = 7 cm Perimeter: ______ cm
6. Trapezium: sides = 5 cm, 8 cm, 6 cm, 9 cm Perimeter: ______ cm

Exercise C – Area Calculations

Find the area of these shapes:

1. Rectangle: length = 12 cm, width = 8 cm Area: ______ cm²
2. Square: side = 9 cm Area: ______ cm²
3. Triangle: base = 10 cm, height = 6 cm Area: ______ cm²
4. Circle: radius = 7 cm (use π = 22/7) Area: ______ cm²
5. Parallelogram: base = 15 cm, height = 8 cm Area: ______ cm²
6. Trapezium: parallel sides = 12 cm and 8 cm, height = 5 cm Area: ______ cm²

Mixed Problems – Regular Shapes

Exercise D – Shape Comparisons

Compare areas and perimeters:

1. Shape A: Square with side 6 cm Shape B: Rectangle with length 8 cm, width 4 cm Which has larger area? ______ Which has larger perimeter? ______
2. Circle: radius = 10 cm Square: side = 10 cm Which has larger area? ______ (use π = 3.14) Which has larger perimeter? ______

Exercise E – Finding Missing Measurements

Use area or perimeter to find missing dimensions:

1. Rectangle: Area = 72 cm², length = 9 cm Width: ______ cm
2. Square: Perimeter = 36 cm Side: ______ cm
3. Circle: Area = 154 cm² (use π = 22/7) Radius: ______ cm
4. Triangle: Area = 24 cm², base = 8 cm Height: ______ cm
5. Parallelogram: Area = 56 cm², height = 7 cm Base: ______ cm

Irregular Shapes

Finding Area of Irregular Shapes

Methods:

1. Divide into regular shapes
2. Count squares on grid paper
3. Subtract areas (for shapes with holes)

Example: L-shaped Figure

Break into two rectangles:

• Rectangle 1: 8 cm × 3 cm = 24 cm²
• Rectangle 2: 5 cm × 4 cm = 20 cm²
• Total Area = 24 + 20 = 44 cm²

Exercise F – Irregular Shapes

Find areas by breaking into regular shapes:

1. T-shaped figure:
   1. Top rectangle: 12 cm × 3 cm
   2. Bottom rectangle: 4 cm × 8 cm Total Area: ______ cm²
2. House shape:
   1. Rectangle base: 10 cm × 8 cm
   2. Triangle roof: base 10 cm, height 6 cm Total Area: ______ cm²
3. L-shaped garden:
   1. Large rectangle: 15 m × 8 m
   2. Small rectangle cut out: 5 m × 3 m Remaining Area: ______ m²
4. Plus sign (+):
   1. Horizontal rectangle: 15 cm × 5 cm
   2. Vertical rectangle: 5 cm × 15 cm
   3. Overlap: 5 cm × 5 cm Total Area: ______ cm² (subtract overlap)

Real Life Problems

Exercise G – School and Classroom

Solve these practical problems:

1. Classroom Floor: A rectangular classroom is 12 meters long and 8 meters wide. What area of tiles is needed to cover the floor? Answer: ______ m²
2. School Compound: A square school compound has perimeter 400 meters. What is the area of the compound? Answer: ______ m²
3. Circular Flower Bed: A circular flower bed has radius 3.5 meters. How much fencing is needed around it? (use π = 22/7) Answer: ______ meters
4. Basketball Court: A rectangular basketball court is 28 meters long and 15 meters wide. What is its area and perimeter? Area: ______ m² Perimeter: ______ m

Exercise H – Home and Garden

Apply to household situations:

1. Rectangular Garden: Mama wants to fence a rectangular garden 20 meters by 15 meters. How much fencing does she need? Answer: ______ meters
2. Circular Pond: A circular fish pond has diameter 14 meters. What is its area? (use π = 22/7) Answer: ______ m²
3. Living Room Carpet: A living room is 6 meters by 4 meters. Carpet costs ₦2,500 per square meter. What is the total cost? Answer: ₦______
4. Triangular Plot: A triangular plot of land has base 50 meters and height 30 meters. What is its area? Answer: ______ m²

Exercise I – Construction and Planning

Solve building-related problems:

1. House Foundation: A house foundation is rectangular, 15 m by 12 m, with a circular pool of radius 3 m inside. What area needs concrete? (use π = 3.14) Answer: ______ m²
2. Parking Lot: A rectangular parking lot is 40 m by 25 m. If each car space is 3 m by 5 m, how many cars can park? Answer: ______ cars
3. Sports Field: A football field is 100 m by 64 m. It needs grass costing ₦500 per m². What is the total cost? Answer: ₦______

Exercise J – Farm and Agriculture

Apply to farming scenarios:

1. Rice Field: A farmer has a rectangular rice field 200 m by 150 m. What is the area in hectares? (1 hectare = 10,000 m²) Answer: ______ hectares
2. Circular Farm: A circular farm has radius 100 meters. How much fencing is needed around it? (use π = 3.14) Answer: ______ meters
3. Mixed Crops: A rectangular farm (80 m × 60 m) is divided equally for maize and yam. What area is used for each crop? Answer: ______ m² each

Answer Key

Exercise B:

1. 26 cm, 2. 28 cm, 3. 24 cm, 4. 88 cm, 5. 38 cm, 6. 28 cm

Exercise C:

1. 96 cm², 2. 81 cm², 3. 30 cm², 4. 154 cm², 5. 120 cm², 6. 50 cm²

Exercise D:

1. Shape A (36 cm² vs 32 cm²), Equal (24 cm each)
2. Circle (314 cm² vs 100 cm²), Circle (62.8 cm vs 40 cm)

Exercise E:

1. 8 cm, 2. 9 cm, 3. 7 cm, 4. 6 cm, 5. 8 cm

Exercise F:

1. 68 cm², 2. 110 cm², 3. 105 m², 4. 100 cm²

Exercise G:

1. 96 m², 2. 10,000 m², 3. 22 meters, 4. 420 m², 86 m

Exercise H:

1. 70 meters, 2. 154 m², 3. ₦60,000, 4. 750 m²

Exercise I:

1. 151.74 m², 2. 66 cars, 3. ₦3,200,000

Exercise J:

1. 3 hectares, 2. 628 meters, 3. 2,400 m² each