A regular triangle ahd a regular quadrilateral share a common side. write a ratio of the area of the rectangle to the area of the triangle

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24-04-2018
Mathematics

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A regular triangle ahd a regular quadrilateral share a common side. write a ratio of the area of the rectangle to the area of the triangle

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Rodiak Rodiak · Answer 1 · 2018-05-06T00:48:05+02:00

Part "share a common side" means that both triangle and quadrilateral have same side length.
Area of regular triangle can be calculated by:
[tex]A= \frac{side*height}{2} \\ \\ A= \frac{a*a* \frac{ \sqrt{3} }{2} }{2} \\ \\ A= \frac{ a^{2} * \sqrt{3} }{4} [/tex]
Area of regular quadrilateral can be calculated by:
[tex]A=side*side \\ \\ A=a*a \\ A= a^{2} [/tex]

Ratio:
[tex] \frac{rectangle}{triangle} = \frac{ a^{2} }{\frac{ a^{2} * \sqrt{3} }{4}} \\ \\ \frac{rectangle}{triangle} = \frac{4a^{2}}{a^{2} * \sqrt{3} } \\ \\ \frac{rectangle}{triangle} = \frac{4}{\sqrt{3}} \\ \\ \frac{rectangle}{triangle} = \frac{4\sqrt{3}}{3} [/tex]