1103055013
Level:
B
The regular pentagon \( ABCDE \) is inscribed in a circle with the center \( S \) (see the picture). Express the measure of the angle \( SAB \).
\( 54^{\circ} \)
\( 72^{\circ} \)
\( 36^{\circ} \)
\( 108^{\circ} \)
Polygons
1103055012
Level:
B
The regular pentagon \( ABCDE \) is inscribed in a circle with the center \( S \) (see the picture). Give the measure of the angle \( ASB \).
\( 72^{\circ} \)
\( 36^{\circ} \)
\( 54^{\circ} \)
\( 108^{\circ} \)
1103055011
Level:
B
The picture shows the regular octagon \( ABCDEFGH \) and the equilateral triangle \( ABJ \). Give the measure of the angle \( JBC \).
\( 75^{\circ} \)
\( 30^{\circ} \)
\( 45^{\circ} \)
\( 60^{\circ} \)
1103055010
Level:
C
In the regular hexagon \( ABCDEF \), \( G \) and \( H \) are the midpoints of \( AB \) and \( CD \). What part of the area of the hexagon is covered by the area of the quadrilateral \( BCHG \)? The area of the quadrilateral corresponds to the shaded region in the figure.
\( \frac5{24} \)
\( \frac15 \)
\( \frac1{28} \)
\( \frac5{36} \)
1103055009
Level:
B
The regular hexagon \( ABCDEF \) is in the picture. The area of the triangle \( ABC \) is \( 10\,\mathrm{cm}^2 \). Calculate the length of the side of the hexagon. Round to one decimal place.
\( 4.8\,\mathrm{cm} \)
\( 23.1\,\mathrm{cm} \)
\( 6.3\,\mathrm{cm} \)
\( 7.2\,\mathrm{cm} \)
1103055008
Level:
B
\( ABCDEF \) is a regular hexagon. (See the picture.) The area of the triangle \( ABC \) is \( 6\,\mathrm{cm}^2 \). Calculate the area of the hexagon.
\( 36\,\mathrm{cm}^2 \)
\( 24\,\mathrm{cm}^2 \)
\( 30\,\mathrm{cm}^2 \)
\( 42\,\mathrm{cm}^2 \)
1003055007
Level:
B
In a regular decagon (\( 10 \) sided polygon) the length of the side is \( 4\,\mathrm{cm} \). Which of the given numbers most accurately expresses fits its area most accurately?
\( 123\,\mathrm{cm}^2 \)
\( 12\,\mathrm{cm}^2 \)
\( 55\,\mathrm{cm}^2 \)
\( 185\,\mathrm{cm}^2 \)
1003055006
Level:
B
A regular pentadecagon (\( 15 \) sided polygon) is inscribed in a circle of radius \( 8\,\mathrm{cm} \). Calculate its area. Round the result to two decimal places.
\( 195.23\,\mathrm{cm}^2 \)
\( 97.62\,\mathrm{cm}^2 \)
\( 13.02\,\mathrm{cm}^2 \)
\( 24.40\,\mathrm{cm}^2 \)
1003055005
Level:
B
The side of a regular hexagon is \( 4\,\mathrm{cm} \) long. Which of the numbers gives the area of the hexagon?
\( 24\sqrt3\,\mathrm{cm}^2 \)
\( 4\sqrt3\,\mathrm{cm}^2 \)
\( 48\sqrt3\,\mathrm{cm}^2 \)
\( 20\sqrt3\,\mathrm{cm}^2 \)
1103055004
Level:
B
A regular pentagon is inscribed in a circle of radius \( 10\,\mathrm{cm} \). Calculate the perimeter of the pentagon. Round the result to two decimal places.
\( 58.78\,\mathrm{cm} \)
\( 5.88\,\mathrm{cm} \)
\( 11.76\,\mathrm{cm} \)
\( 80.90\,\mathrm{cm} \)