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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.
    $P=18\sqrt{3}cm$
    $P=36\sqrt{3}cm$
    $P=12\sqrt{3}cm$
    $P=6\sqrt{3}cm$

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