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• Geometry
• Polygons
• Area and perimeter of regular polygons

# Area and perimeter of regular polygons

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•  Question 1: 1 pts Area of regular Polygon = $\dfrac{{\mbox{perimeter}}\cdot {\mbox{apothem}}}{2}$
•  Question 2: 1 pts The perimeter of the hexagon is three times the diameter of the circle.
•  Question 3: 1 pts The perimeter of a regular heptagon is $63 cm.$ What is the length of each side?
 $7 cm$ $3 cm$ $21 cm$ $9 cm$
•  Question 4: 1 pts Find the perimeter of a nonagon with side length of $21cm.$
 $81cm$ $132cm$ $164cm$ $189cm$
•  Question 5: 2 pts Which expression can be used to find the area of the regular dodecagon, if the radius of described circle around the twelfth has length 6 cm.
 $A=\dfrac{12\cdot 6^{2}\cdot \sin 30^{\circ}}{2}$ $A=\dfrac{12\cdot 12^{2}\cdot \sin 30^{\circ}}{2}$ $A=\dfrac{12\cdot 6^{2}\cdot \sin 60^{\circ}}{2}$ $A=\dfrac{6\cdot 12^{2}\cdot \sin 60^{\circ}}{2}$
•  Question 6: 2 pts Find the area of a regular pentagon each of whose sides measures $6 cm$ and the radius of the inscribed circle is $3.5 cm.$
Area$=$
•  Question 7: 2 pts The area of a regular pentagon is $440.44 in^{2}$ and the perimeter is $80 in.$ Find the length of the apothem of the pentagon.
 $10.01$ $11.011$ $10.011$ $10.1$
•  Question 8: 2 pts The following expression can be used to find the area of octagon:$$BM=\dfrac{a}{\sqrt{2}}; OL=ON+LN=ON+BM$$ $$\Right arrow OL=\left(\dfrac{a}{2}+\dfrac{a}{\sqrt{2}}\right)$$ $$A=8\cdot A_{\vartriangle OAB}=8\cdot \dfrac{AB\cdot OL}{2}=4\cdot a\cdot \left(\dfrac{a}{2}+\dfrac{a}{\sqrt{2}}\right)=2a^{2}\cdot\left(1+\sqrt{2}\right)$$
•  Question 9: 3 pts Find the area of the regular polygon shown on the picture.
 $42.35cm^{2}$ $112.27cm^{2}$ $232.57cm^{2}$ $185.29cm^{2}$
•  Question 10: 3 pts What is the area of the hexagon if its radius of inscribed circles is doubled? Let the original area be $A sq. units$
 $4A sq. units$ $8A sq. units$ $12A sq. units$ $16A sq. units$
•  Question 11: 3 pts Find the length of the apothem in the regular dodecagon. Round your answer to the nearest hundredth.
 $14.49cm$ $12.23cm$ $11.39cm$ $13.49cm$
•  Question 12: 3 pts Find the perimeter of the "star" shown on the picture.
 $P=18\sqrt{3}cm$ $P=36\sqrt{3}cm$ $P=12\sqrt{3}cm$ $P=6\sqrt{3}cm$