Circles

1103077202

Level: 
C
Let \( ABCDEF \) be a regular hexagon. Six circles of equal radii are drawn touching each other with their centres at the hexagon vertices (see the picture). Calculate the area of the coloured region inside the hexagon if you know that the perimeter of the hexagon \( ABCDEF \) is \( 36\,\mathrm{cm} \). Round the result to two decimal places.
\( 36.98\,\mathrm{cm}^2 \)
\( 93.53\,\mathrm{cm}^2 \)
\( 65.26\,\mathrm{cm}^2 \)
\( 25.37\,\mathrm{cm}^2 \)

1103256901

Level: 
C
The farmer tied two goats on the meadow. The distance of the stakes \( K_1 \), \( K_2 \) to which the goats are tied is \( 5\,\mathrm{m} \) and the ropes have lengths of \( 3\,\mathrm{m} \) and \( 4\,\mathrm{m} \). What is the area of the grassland which is common for both goats? Round the result to two decimal places.
\( 6.64\,\mathrm{m}^2 \)
\( 0.57\,\mathrm{m}^2 \)
\( 0.35\,\mathrm{m}^2 \)
\( 1.52\,\mathrm{m}^2 \)