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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 = \mboxperimeter⋅\mboxapothem2\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 63cm.63 cm. What is the length of each side?
    7cm7 cm
    3cm3 cm
    21cm21 cm
    9cm9 cm
  • Question 4:
    1 pts
    		Find the perimeter of a nonagon with side length of 21cm.21cm.
    81cm81cm
    132cm132cm
    164cm164cm
    189cm189cm
  • 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=12⋅62⋅sin⁡30∘2A=\dfrac{12\cdot 6^{2}\cdot \sin 30^{\circ}}{2}
    A=12⋅122⋅sin⁡30∘2A=\dfrac{12\cdot 12^{2}\cdot \sin 30^{\circ}}{2}
    A=12⋅62⋅sin⁡60∘2A=\dfrac{12\cdot 6^{2}\cdot \sin 60^{\circ}}{2}
    A=6⋅122⋅sin⁡60∘2A=\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 6cm6 cm and the radius of the inscribed circle is 3.5cm.3.5 cm.
    Area==
  • Question 7:
    2 pts
    		The area of a regular pentagon is 440.44in2440.44 in^{2} and the perimeter is 80in.80 in. Find the length of the apothem of the pentagon.

    10.0110.01

    11.01111.011

    10.01110.011

    10.110.1

  • Question 8:
    2 pts
    		The following expression can be used to find the area of octagon:BM=a2;OL=ON+LN=ON+BM BM=\dfrac{a}{\sqrt{2}}; OL=ON+LN=ON+BM \RightarrowOL=(a2+a2)\Right arrow OL=\left(\dfrac{a}{2}+\dfrac{a}{\sqrt{2}}\right) A=8⋅A△OAB=8⋅AB⋅OL2=4⋅a⋅(a2+a2)=2a2⋅(1+2)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.
    42.35cm242.35cm^{2}
    112.27cm2112.27cm^{2}
    232.57cm2232.57cm^{2}
    185.29cm2185.29cm^{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 Asq.unitsA sq. units

    4Asq.units4A sq. units

    8Asq.units8A sq. units

    12Asq.units12A sq. units

    16Asq.units16A sq. units

  • Question 11:
    3 pts
    		Find the length of the apothem in the regular dodecagon. Round your answer to the nearest hundredth.
    14.49cm14.49cm
    12.23cm12.23cm
    11.39cm11.39cm
    13.49cm13.49cm
  • Question 12:
    3 pts
    		Find the perimeter of the "star" shown on the picture.
    P=183cmP=18\sqrt{3}cm
    P=363cmP=36\sqrt{3}cm
    P=123cmP=12\sqrt{3}cm
    P=63cmP=6\sqrt{3}cm

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