B3 Given a triangle $\triangle A B C$ (see the figure), where $z=4 \mathrm{~cm}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf2b29f7493f2ef25deg-4.jpg?height=371&width=928&top_left_y=771&top_left_x=607)

A How many triangles are there in the figure?

B What is the name of the triangle $\triangle E B C$ based on the lengths of its sides?

C What is the name of the triangle $\triangle D E C$ based on the lengths of its sides?

D Calculate the area of the triangle $\triangle A B C$! Round the result to the nearest cm ${ }^{2}$.
B3 In the figure, there are 6 triangles: $\triangle A B C, \triangle A E C, \triangle D B C, \triangle A D C, \triangle D E C, \triangle E B C$. Triangle $\triangle E B C$ is isosceles and equilateral, while triangle $\triangle D E C$ is isosceles. The area of triangle $\triangle A B C$ can be calculated using the formula $S_{\triangle}=\frac{\overline{A B} \cdot v_{\triangle A B C}}{2}$, where $\overline{A B}=3 z=12 \mathrm{~cm}$ and $v_{\triangle A B C}=v_{\triangle E B C}=$ $\frac{z \sqrt{3}}{2}=\frac{4 \sqrt{3}}{2}=2 \sqrt{3} \mathrm{~cm}$. The area of triangle $\triangle A B C$ is $S_{\triangle A B C}=\frac{\overline{A B \cdot v} \cdot \mathrm{v}_{\triangle A B C}}{2}=\frac{12 \mathrm{~cm} \cdot 2 \sqrt{3} \mathrm{~cm}}{2}=$ $12 \sqrt{3} \mathrm{~cm}^{2} \approx 21 \mathrm{~cm}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf2b29f7493f2ef25deg-7.jpg?height=66&width=1664&top_left_y=224&top_left_x=253)

B Triangle $\triangle E B C$ is isosceles and equilateral. ................................ $1 \mathbf{t}$

C Triangle $\triangle D E C$ is isosceles. . ..................................................... $1 \mathbf{t}$

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf2b29f7493f2ef25deg-7.jpg?height=52&width=1664&top_left_y=431&top_left_x=253)

Determination of the height of triangle $\triangle A B C: 2 \sqrt{3} \mathrm{~cm} \approx 3.5 \mathrm{~cm} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots \mathbf{1 t}$

Calculation of the area of triangle $\triangle A B C: 21 \mathrm{~cm}^{2} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots \mathbf{t}$

Note: If the area is not rounded to $\mathrm{cm}^{2}$, deduct 1 point from the contestant.