Question

Given parallelogram PQRS with P(-4,-2), Q(-2,3), R(4,3) and S(2,-2). Find the area of PQRS in sq. Units

Answer 1

To find the area of parallelogram PQRS, we can use the formula:

Area = base * height

First, let's find the length of the base. We can calculate the distance between points P(-4, -2) and Q(-2, 3) using the distance formula:

d(PQ) = √[(x2 - x1)² + (y2 - y1)²]
= √[(-2 - -4)² + (3 - -2)²]
= √[(-2 + 4)² + (3 + 2)²]
= √[2² + 5²]
= √[4 + 25]
= √29

So, the base of parallelogram PQRS is √29.

Next, let's find the height of the parallelogram. We can calculate the distance between points P(-4, -2) and S(2, -2) using the distance formula:

d(PS) = √[(x2 - x1)² + (y2 - y1)²]
= √[(2 - -4)² + (-2 - -2)²]
= √[(2 + 4)² + (-2 + 2)²]
= √[6² + 0²]
= √[36]
= 6

So, the height of parallelogram PQRS is 6.

Now, we can calculate the area using the formula:

Area = base * height
= √29 * 6
= 6√29

Therefore, the area of parallelogram PQRS is 6√29 sq. units.