B3. Šivilja had a piece of fabric in the shape of a square with a side length of $8 \mathrm{~cm}$. From it, she cut out two isosceles trapezoids and obtained a loop (see the image, the loop is represented by the shaded area). The lengths of the bases of the cut trapezoids are $8 \mathrm{~cm}$ and $2 \mathrm{~cm}$, and the height is $3 \mathrm{~cm}$.

A What is the area of one of the cut trapezoids in square centimeters?

B What is the area of the loop in square centimeters?

![](https://cdn.mathpix.com/cropped/2024_06_07_474093644c4c736111d0g-4.jpg?height=408&width=414&top_left_y=224&top_left_x=1506)

C What fraction of the area of the square does the area of the loop represent? Express the result as a decimal number to 2 decimal places.
B3. The area of the cut-out trapezoid is calculated using the formula $S=\frac{(a+c) v}{2}$, where $a=8 \mathrm{~cm}, c=$ $2 \mathrm{~cm}$ and $v=3 \mathrm{~cm}$. The area is $S=15 \mathrm{~cm}^{2}$. The area of the loop represents the remaining area of the square with a side of $8 \mathrm{~cm}$, after the needle has cut out two isosceles trapezoids: $S_{\text {loop }}=$ $S_{\text {square }}-2 \cdot S_{\text {trapezoid }}=64 \mathrm{~cm}^{2}-2 \cdot 15 \mathrm{~cm}^{2}=34 \mathrm{~cm}^{2}$. The area of the loop represents $\frac{34 \mathrm{~cm}^{2}}{64 \mathrm{~cm}^{2}}=$ $0.5313 \approx 0.53$ of or $53 \%$ of the area of the square.

![](https://cdn.mathpix.com/cropped/2024_06_07_474093644c4c736111d0g-6.jpg?height=63&width=1659&top_left_y=2581&top_left_x=256)

B Calculation of the area of the loop using the formula or by counting squares: $S=34 \mathrm{~cm}^{2} \ldots . \mathbf{1 p}$ Written answer, e.g.: The loop has an area of $34 \mathrm{~cm}^{2} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ p

C Calculated and correctly rounded proportion of the area of the loop relative to the area of the square: 0.53 or $53 \%$. $2 \mathbf{p}$ Note: An inappropriate or incorrect rounding will earn the contestant only 1 point.