Question

Find the area of a rhombus with a perimeter of 20 meters and a diagonal of 8 meters

Answer 1

All four sides are equal, so each side is 5 m.
Also the diagonals right-bisect each other to form 4 congruent right-angled triangles
Consider one of thes.
The hypotenuse is 5, one leg is 4 , so the other must be 3 by Pythagoras.
Area of one of those = (1/2)(3)(4) = 6

So the whole rhombus has area of 24 m^2

or

the area of a rhomus = (1/2)(product of their diagonals)
= (1/2)(6)(8) = 24

Answer 2

The perimeter of a rhombus is 40 cm and the distance between a pair of parallel side is 5.6 cm. If the length of one of its diagonals is 7 cm, find the length of the other diagonal.