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  • Geometry
  • Quadrilaterals
  • Triangular pyramid

Triangular pyramid

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  • Question 1:
    1 pts
    		The surface area of the regular triangular pyramid shown on the picture is $A=\left(\dfrac{5^{2}\sqrt{3}}{4}+3\cdot\dfrac{5\cdot 10}{2}\right)cm^{2}$
  • Question 2:
    1 pts
    		The following expression can be used to find the height of the regular triangular pyramid shown on the picture.$$ 9^{2}=H^{2}+(\sqrt{3})^{2}$$
  • Question 3:
    1 pts
    		The following expression can be used to find the volume of the regular triangular pyramid shown on the picture. $$V=\left(\dfrac{\left(6\sqrt{3}\right)^{2}\sqrt{3}}{4}\cdot 4 \right)cm^{3}$$
  • Question 4:
    1 pts
    		The following expression can be used to find the length of base edges of the regular triangular pyramid shown on the picture. $8^{2}=4^{2}+x^{2} $ $\mbox{base edge}=\dfrac{6x}{\sqrt{3}} $
  • Question 5:
    2 pts
    		Determine the volume and surface area of a regular triangular pyramid having a base edge $a=10 cm$ and a lateral edge $b = 13 cm.$
  • Question 6:
    2 pts
    		Calculate the volume of a regular triangular pyramid whose height is equal to the length of the base edges $11 cm.$

    $V=\dfrac{1331\sqrt{3}}{12}cm^{3}$

    $V=\dfrac{985\sqrt{3}}{12}cm^{3}$

    $V=\dfrac{613\sqrt{3}}{8}cm^{3}$

    $V=\dfrac{613\sqrt{3}}{4}cm^{3}$

  • Question 7:
    2 pts
    		�Area of the whole surface of the regular tetrahedron $$A=a^{2}\sqrt{3}$$
  • Question 8:
    2 pts
    		Volume of the regular tetrahedron $$V=\dfrac{a^{3}\sqrt{2}}{\sqrt{3}}$$
  • Question 9:
    3 pts
    		Which expression can be used to find the height of regular triangular pyramid if her surface area is $112\sqrt{3}cm^{2},$ and the length of base edge is $8cm.$
    $H^{2}=\left(4\sqrt{3}\right)^{2}+\left(\dfrac{4\sqrt{3}}{3}\right)^{2}$
    $H^{2}=\left(8\sqrt{3}\right)^{2}-\left(\dfrac{4\sqrt{3}}{3}\right)^{2}$
    $H^{2}=\left(6\sqrt{3}\right)^{2}+\left(\dfrac{4\sqrt{3}}{3}\right)^{2}$
    $H^{2}=\left(2\sqrt{3}\right)^{2}-\left(\dfrac{3\sqrt{3}}{4}\right)^{2}$
  • Question 10:
    3 pts
    		The area of total lateral surface of the triangular pyramid is $162 cm^{2}.$ Find the length of base edge of that pyramid if the base edge is equal to apothem.

    $4\sqrt{5}cm$

    $6\sqrt{3}cm$

    $4\sqrt{2}cm$

    $3\sqrt{6}cm$

  • Question 11:
    3 pts
    		Find the volume of the triangular pyramid shown on the picture .
    $V=175\sqrt{3}m^{3}$
    $V=196\sqrt{3}m^{3}$
    $V=221\sqrt{3}m^{3}$
    $V=343\sqrt{3}m^{3}$
  • Question 12:
    3 pts
    		Find the volume of the triangular pyramid shown on the picture .
    $V=545\sqrt{3}m^{3}$
    $V=235\sqrt{3}m^{3}$
    $V=425\sqrt{3}m^{3}$
    $V=700\sqrt{3}m^{3}$

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