Question

How do you calculate the area of a parallelogram if only two diagonals are given?

Answer 1

Hint: We start solving the problem by recalling the fact that the diagonals in a parallelogram bisect each other. We then assume the lengths of the diagonals of the parallelogram and then draw a figure representing the given information. We then check whether the area of the diagonal can be found from the figure which gives the required conclusion for the given statement.

Complete step by step answer:
According to the problem, we are asked to check whether we can find the area of a parallelogram if only two diagonals are given.
We know that the diagonals in a parallelogram bisect each other. Let us assume the length of the diagonals be 2a and 2b. Now, let us draw the figure representing the given information.

We can see that the area of the parallelogram can be found by the sum of the areas of the four triangles formed.
We know that the area of the triangle is $\dfrac{1}{2}ab\sin \theta $, which tells us that we need the value of angle between the diagonals to get the required area of the parallelogram.
$\therefore $ We have got the conclusion that we cannot find the area of the parallelogram if only lengths of diagonals are given.

Note:
Whenever we get this type of problem, we first draw the figure following all the properties of the figure, which helps us to get the required answer. We should keep in mind that the angle between the diagonals in a parallelogram is not constant while solving this problem. Similarly, we can expect problems to check whether we can find the area of the rhombus if lengths of its diagonals are given.