B4. Soboslikar has painted over a wall that has the shape of an isosceles triangle with a base of $32 \mathrm{dm}$ and legs of $2 \mathrm{~m}$. He painted $25 \%$ of the wall with blue paint, and the rest of the wall with white paint. How many square meters of the wall did he paint with blue paint?

## 9th Mathematics Knowledge Competition for Vocational School Students  Regional Competition, April 1, 2009

## Solutions to Problems and Scoring

A competitor who arrives at the solution by any correct method (even if not anticipated by the scoring guide) receives all possible points.

For a correct method, any procedure that

- sensibly takes into account the wording of the problem,
- leads to the solution of the problem,
- is mathematically correct and complete.

$V$ in the table, the correct answers to the multiple-choice questions are recorded. Each correct answer is scored 2 points, an incorrect answer $-0.5$ points, and if the question is not answered, 0 points.

| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| C | C | A | D | A | C | C | D | B | A |
B4. Calculated height of the triangle: $v=\sqrt{20^{2}-16^{2}}=\sqrt{144}=12 \mathrm{dm} \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .2$ points Calculated area of the triangle: $S=\frac{32 \cdot 12}{2}=192 d m^{2} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ point

![](https://cdn.mathpix.com/cropped/2024_06_07_1ce1e4422095ce2d7960g-5.jpg?height=69&width=1690&top_left_y=2487&top_left_x=223)
Answer: He painted $0.48 \mathrm{~m}^{2}$ with blue color \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (The student gets the last point for the correct conversion of units.)