Question

Find the ratio of the total area of the grid shown below to the approximate area covered by the pizza if the side of smallest square is 1 cm and each such square is congruent?
(4 marks)

Answer 1

Side of the smallest square = 1 cm
⇒ Area of one such square = 1 × 1 = 1 $c{m}^2$
⇒ Total area of the square grid = 7 × 7 = 49 $c{m}^2$
(1 mark)

Let us count the squares that are completely covered, half covered and so on. Also, these can be marked as shown below:

Now, we need to write the number of squares that are covered by the shape.
(1 mark)

Therefore, the approximate area of the given shape
= 12(1) + 0( <!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> $\frac{1}{2}$) + 9(1) + 8(0)
= 12 + 0 + 9 + 0
= 21 $c{m}^2$
(1 mark)

Hence, the required ratio = $\frac{49}{21}$ = $\frac{7}{3}$
(1 mark)