Measuring Area (Grade 10 NSC Matric Mathematical Literacy): Revision Notes

Worked Example 1: Rectangular patio using a grid

Let's estimate the area of Mr and Mrs Dlamini's rectangular patio where each grid square represents 1 cm².

Solution:

• Count each square systematically and mark it as you go
• The patio is 5 blocks wide and 6 blocks high
• Total blocks = $6 \times 5 = 30$ blocks
• Since each block = 1 cm², the area = 30 cm²

Worked Example 2: Triangular garden using a grid

Now let's estimate the area of a triangular garden using the same grid method.

Solution: When estimating a triangle's area with a grid:

• First, count all the complete blocks inside the triangle = 18 blocks
• Next, count the half-blocks that fit inside = 4 half-blocks = 2 whole blocks
• Count remaining partial blocks and estimate = approximately 4½ whole blocks
• Total estimated area = $18 + 2 + 4.5 =$ 24.5 cm²

Worked Example 3: Circular pond using a grid

For a circular fish pond, the grid method becomes an estimation tool since circles don't fit neatly into square grids.

Solution:

• Each piece of the circle takes up approximately three-quarters of a square
• There are 4 such squares, so: $4 \times \frac{3}{4} = 3$ whole blocks
• Estimated area = 3 cm²

Worked Example 4: Using formulae for basic shapes

Calculate the area of these three shapes:

Solutions:

a) Rectangle (Patio):

• Area = $\text{Length} \times \text{Width}$
• Area = $5 \text{ cm} \times 6 \text{ cm} =$ 30 cm²

b) Triangle (Garden):

• Area = $\frac{1}{2} \times \text{Base} \times \text{Perpendicular Height}$
• Area = $\frac{1}{2} \times 12 \text{ cm} \times 4 \text{ cm} =$ 24 cm²

c) Circle (Pond):

• Area = $\pi \times \text{radius}^2$
• Area = $3.142 \times (1 \text{ cm})^2$
• Area = $3.142 \times 1 \text{ cm}^2 =$ 3.142 cm²

Worked Example 5: Complex shapes

Sometimes you'll encounter complex shapes that need to be broken down into simpler parts.

For a trapezoidal table shape with dimensions 70 cm height, 0.9 m and 500 mm widths:

Solution approach:

1. Convert all units to the same measurement (e.g., all in cm)
2. Break the complex shape into simpler shapes (rectangles and triangles)
3. Calculate each area separately
4. Add all areas together

Worked Example 6: Real-world application

A coin has a circular shape with a square cut out from the middle.

Problem: If the circle diameter is 3 cm and the square side is 0.9 cm, find the remaining area.

Solution:

1. Calculate circle area:
   • Radius = $3 \div 2 = 1.5$ cm
   • Circle area = $\pi \times (1.5)^2 = 3.142 \times 2.25 = 7.0695$ cm²
2. Calculate square area:
   • Square area = $(0.9)^2 = 0.81$ cm²
3. Find remaining area:
   • Remaining area = $7.0695 - 0.81 = 6.2595 \approx$ 6.3 cm²