Task 5. Determine the area of the triangle in the drawing (without measuring the necessary lengths), if each of the small squares has an area of $1 \mathrm{~cm}^{2}$.
Solution. The area of the triangle will be calculated as the difference between the area of the square and the triangles $\triangle A D B, \triangle B I F$ and $\triangle D F G$.

![](https://cdn.mathpix.com/cropped/2024_06_05_a73f0c01d543f9cc2089g-05.jpg?height=313&width=368&top_left_y=1264&top_left_x=1114)

![](https://cdn.mathpix.com/cropped/2024_06_05_a73f0c01d543f9cc2089g-05.jpg?height=387&width=447&top_left_y=1633&top_left_x=250)

The areas of the triangles $\triangle A D B$, $\triangle B I F$ and $\triangle D F G$ will be calculated as half of the areas of the rectangles $A B C D$, $B I F H$ and $D E F G$ respectively.

Thus, the area of the desired triangle is

$$
P=42-\frac{1}{2}(5 \cdot 4+2 \cdot 6+7 \cdot 2)=42-23=19 \mathrm{~cm}^{2}
$$

## VI Section