Question 6

In the adjoining figure, the distance between any two adjacent dots is 1 cm. The area of the shaded region (in $$\text{cm}^2$$) is

Solution

Every corner of the shaded figure sits on a dot of the grid, so the dot rule for area can be used, which says the area equals the number of dots strictly inside, plus half the number of dots on the boundary, minus 1. This figure has 6 dots inside it and 21 dots on its boundary, so the area is $$6 + \frac{21}{2} - 1 = \frac{31}{2}$$ square cm.

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In the adjoining figure, the distance between any two adjacent dots is 1 cm. The area of the shaded region (in $$\text{cm}^2$$) is

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