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

Aregular triangle ahd a regular quadrilateral share

Ответ:

winterblackburn78

14.03.2022

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

Ratio:
$\frac{rectangle}{triangle} = \frac{ a^{2} }{\frac{ a^{2} * \sqrt{3} }{4}} \\ \\ \frac{rectangle}{triangle} = \frac{4a^{2}}{a^{2} * \sqrt{3} } \\ \\ \frac{rectangle}{triangle} = \frac{4}{\sqrt{3}} \\ \\ \frac{rectangle}{triangle} = \frac{4\sqrt{3}}{3}$