An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is $3 \mathrm{c}{\mathrm{m}}^2,$ then the area of the hexagon is

Quantity $1$: Area of square is $324 {\mathrm{cm}}^2$, whose perimeter is equal to perimeter of rectangle. Length of the rectangle is $4 \mathrm{cm}$ more than breadth of the rectangle. Find the area of rectangle.

Quantity $2$: $320 {\mathrm{cm}}^2$.

The perimeter and the breadth of a rectangle are $52 cm$ and $12 cm$ respectively. Find its area in $c{m}^2$.

A path of uniform width runs round the inside of a rectangular field $38 \mathrm{m}$ long and $32 \mathrm{m}$ width, if the path occupies $600 {\mathrm{m}}^2$ then the width of the path is

The length of rectangle is $80\%$ of diagonal of square of area $1225 {\mathrm{m}}^2$, then find area of rectangle, if it's perimeter is $94\sqrt{2} \mathrm{m}$.