KCSE 2025 Maths P1 Q5 — Area by Counting Squares

KCSE 2025 Form 4 Measurement

Published

The Question

“A rectangular farm measuring 210 m by 120 m is drawn on a grid of 1 cm squares. A dotted section inside the farm is flooded. Estimate, in square metres, the area of the farm that is not flooded.”

1

Find what one square represents

Work out the scale from the sides of the farm. The 210 m length is spread across seven grid squares and the 120 m width across four grid squares, so along each direction one square stands for 30 metres on the ground. That means one full grid square represents a 30 m by 30 m patch of land.

210÷7=30 m,120÷4=30 m210 \div 7 = 30 \text{ m}, \quad 120 \div 4 = 30 \text{ m}
30×30=900 m2 per square30 \times 30 = 900 \text{ m}^{2} \text{ per square}
2

Find the total area of the farm

The whole farm is a rectangle, so multiply its length by its width. You can also check this by counting the grid: seven squares by four squares gives twenty-eight squares, and each square is 900 square metres, which agrees.

210×120=25,200 m2210 \times 120 = 25{,}200 \text{ m}^{2}
7×4×900=28×900=25,200 m27 \times 4 \times 900 = 28 \times 900 = 25{,}200 \text{ m}^{2}
3

Count the flooded squares

The flooded region has an irregular shape, so estimate its area by counting the grid squares it covers. Use the standard rule: count a square only when the flooded part fills at least half of it, and ignore squares that are less than half covered. Counting this way gives about eleven squares.

11×900=9,900 m211 \times 900 = 9{,}900 \text{ m}^{2}

The half-square rule keeps the estimate fair: over-counted and under-counted squares roughly cancel out.

4

Subtract to find the un-flooded area

The area that is not flooded is simply the whole farm minus the flooded part. Take the flooded estimate away from the total area.

25,200−9,900=15,300 m225{,}200 - 9{,}900 = 15{,}300 \text{ m}^{2}

Final Result

The area of the farm that is not flooded is approximately 15,300 square metres.

Why this method works

Counting squares works because the grid divides the shape into equal, measurable pieces of land, each worth a fixed area. An irregular flooded region cannot be found with a neat formula, but adding up whole squares it covers approximates it well. The half-covered rule is the key idea: squares that are more than half full are counted whole while those less than half full are dropped, so the small pieces you add balance the small pieces you leave out, and the estimate stays close to the true area. Subtracting the flooded estimate from the exact rectangle area then leaves the un-flooded area.

✓

9,900 + 15,300 = 25,200, which matches the total farm area, so the two parts add back correctly. Because this is an estimate, any answer close to 15,300 square metres is accepted.