Question

Find the areas of the following figure by counting squares.

Answer 1

Hint: In this question, redraw the figure by naming the squares. Then find the number of fully-filled squares, half-filled squares, more than half-filled squares and less than half-filled squares and its area which will lead us to the final required answer. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
First of all, we will redraw and name the squares in the given figure as:

Then, we will count the squares as
1. Fully filled squares
2. Hal-filled squares
3. More than half filled squares
4. Less than half filled squares
And then we will calculate the area by counting fully filled squares as one square unit area, half-filled squares as half square unit area, more than half-filled squares as one square unit area and less than half-filled squares as zero square unit area.

Clearly from the redrawn figure, we have
1. Fully filled squares
Here 17,24,25,26,33,34 and 41 are fully filled squares. Therefore, fully-filled squares = 7. Hence, area of fully filled squares = 7 squares units.
2. Half-filled squares
Here there are no exactly half-filled squares. Therefore, half-filled squares = 0. Hence, the area of half-filled squares = 0 squares units.
3. More than half-filled squares
Here 16,18,19,20,23,27,31,32,35,39,40 and 42 are more than half-filled squares. Therefore, more than half-filled squares = 12. Hence, an area of more than half-filled squares = 12 square units.
4. Less than half-filled squares
Here the squares with numbers 10,11,28,30,48 and 49 are less than half-filled squares. Therefore, less than half-filled squares = 6. Hence, area of less than half-filled squares = 0 square units.
We know that the area of figure by complete square method = area of the fully filled squares + area of half-filled squares + area of more than half-filled squares + area of less than half filled squares
Therefore, area of given figure by complete square method = 7 + 0 + 12 + 0 = 19 square units.
Thus, the required area of the given figure is 19 square units.

Note: In complete square method, we will calculate the area by the counting fully filled squares as one square unit area, half-filled squares as half square unit area, more than half-filled squares as one square unit area and less than half-filled squares as zero square unit area.