On a squared paper, draw (i) a rectangle, (ii) a triangle (iii) any irregular closed figure. Find the approximate area of each by counting the number of squares complete, more than half and exactly half.

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Solution

(i) A rectangle: This contains 18 complete squares.
If we assume that the area of one complete square is 1 cm², then the area of this rectangle will be 18 cm².

(ii) A triangle: This triangle contains 4 complete squares, 6 more than half squares and 6 less than half squares.
If we assume that the area of one complete square is 1 cm², then the area of this shape = (4 + 6 $\times$ 1) = 10 cm²

(iii) Any irregular figure: This figure consists of 10 complete squares, 1 exactly half square, 7 more than half squares and 6 less than half squares.
If we assume that the area of one complete square is 1 cm², then the area of this shape = (10 + $1 \times \frac{1}{2}$ + 7 $\times$ 1) = 17.5 cm²

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