Question

What expression in terms of x can be used to represent the area of parallelogram PQRS?

There is a parallelogram PQRS in which the diagonal PR and the diagonal QS bisect each other into two equal parts at right angle . Each part of both the diagonals has a length 5x.

Answer 1

The expression in terms of x that represents the area of parallelogram PQRS is A = 25x^2.

Step-by-step explanation:

To find the area of parallelogram PQRS, we can use the formula A = base x height. In this case, the base of the parallelogram is one of the equal parts of the diagonal PR, which has a length of 5x. The height of the parallelogram is one of the equal parts of the diagonal QS, which also has a length of 5x. Therefore, the expression in terms of x that represents the area of parallelogram PQRS is A = (5x) x (5x) = 25x^2.

Answer 2

`Area = (25x^2)/(2)`

Step-by-step explanation:

Given

Shape: Parallelogram

`PR = 5x`

`QS = 5x`

`\theta = 90`

Required

Find the area of the parallelogram

Because we were given the measure of the diagonals, the area is:

`Area = (1)/(2) * PR * QS * \sin \theta`

This gives:

`Area = (1)/(2) * 5x * 5x * \sin \ 90`

`Area = (1)/(2) * 5x * 5x * 1`

`Area = (1)/(2) * 25x^2`

`Area = (25x^2)/(2)`