B1. Let the parallelogram have a side length of $a=13 \mathrm{~m}$ and an internal angle of $\alpha=60^{\circ}$. The perimeter of the parallelogram measures $58 \mathrm{~m}$. The parallelogram is the base of a right prism. The height of the prism is equal to the length of the diagonal $f$ of the given parallelogram. Accurately calculate the surface area and volume of the prism.
B1. The side length $b=16 \mathrm{~m}$ of the parallelogram is calculated from its perimeter. Using the sine function, we calculate the height on the base $a, v_{a}=b \sin 60^{\circ}=8 \sqrt{3} \mathrm{~m}$. We calculate the area of the base $O=a v_{a}=104 \sqrt{3} \mathrm{~m}^{2}$. Using the cosine rule $f^{2}=a^{2}+b^{2}-2 a b \cos \alpha$, we calculate the length of the diagonal, which is equal to the height of the prism $v=\sqrt{217} \mathrm{~m}$. We calculate the lateral surface area $S=o v=58 \sqrt{217} \mathrm{~m}^{2}$. We accurately write the calculation of the surface area $P=2 O+S=(208 \sqrt{3}+58 \sqrt{217}) \mathrm{~m}^{2}$. We also write the calculation of the volume $V=O v=104 \sqrt{651} \mathrm{~m}^{3}$.

Calculation of the side length $b=16 \mathrm{~m}$. 1 point

Calculation of the height of the parallelogram $v_{a}=b \sin 60^{\circ}=8 \sqrt{3} \mathrm{~m}$ 1 point

Calculation of the area of the base $O=a v_{a}=104 \sqrt{3} \mathrm{~m}^{2}$. 1 point

Application of the cosine rule $f^{2}=a^{2}+b^{2}-2 a b \cos \alpha$ $1^{*}$ point

![](https://cdn.mathpix.com/cropped/2024_06_07_5bf9d67aee417dc7ba6ag-22.jpg?height=65&width=1731&top_left_y=2109&top_left_x=174)

![](https://cdn.mathpix.com/cropped/2024_06_07_5bf9d67aee417dc7ba6ag-22.jpg?height=52&width=1727&top_left_y=2167&top_left_x=176)

![](https://cdn.mathpix.com/cropped/2024_06_07_5bf9d67aee417dc7ba6ag-22.jpg?height=57&width=1727&top_left_y=2213&top_left_x=176)
Calculation of the volume $V=104 \sqrt{651} \mathrm{~m}^{3}$ 1 point