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
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.
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 the distance between points P and Q, and the height is the distance between points P and S.
Step 1: Find the length of PQ (base)
Use the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Given points P(-4,-2) and Q(-2,3), substitute the values into the distance formula:
d = √[(-2 - (-4))² + (3 - (-2))²]
d = √[(-2 + 4)² + (3 + 2)²]
d = √[2² + 5²]
d = √[4 + 25]
d = √29
So, the length of PQ is √29.
Step 2: Find the height of parallelogram P (height)
Use the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Given points P(-4,-2) and S(2,-2), substitute the values into the distance formula:
d = √[(2 - (-4))² + (-2 - (-2))²]
d = √[(2 + 4)² + (0)²]
d = √[6²]
d = 6
So, the height of PQRS is 6.
Step 3: Calculate the area of PQRS
Using the formula A = base x height:
A = √29 x 6
A = 6√29
Therefore, the area of PQRS is 6√29 square units.