Question

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

Answer 1

Part "share a common side" means that both triangle and quadrilateral have same side length.
Area of regular triangle can be calculated by:

`A= (side*height)/(2) \\ \\ A= (a*a* ( √(3) )/(2) )/(2) \\ \\ A= ( a^(2) * √(3) )/(4)`
Area of regular quadrilateral can be calculated by:

`A=side*side \\ \\ A=a*a \\ A= a^(2)`

Ratio:

`(rectangle)/(triangle) = ( a^(2) )/(( a^(2) * √(3) )/(4)) \\ \\ (rectangle)/(triangle) = (4a^(2))/(a^(2) * √(3) ) \\ \\ (rectangle)/(triangle) = (4)/(√(3)) \\ \\ (rectangle)/(triangle) = (4√(3))/(3)`