Find the area and perimeter of square CDEF with vertices C(7,6), D(–8,6), E(–8,–9), and F(7,–9).
Question
Find the area and perimeter of square CDEF with vertices C(7,6), D(–8,6), E(–8,–9), and F(7,–9).
Solution
To find the area and perimeter of the square, we first need to calculate the length of one side. We can do this by using the distance formula between two points, which is √[(x₂ - x₁)² + (y₂ - y₁)²].
Let's use points C and D to calculate the length of one side.
C(7,6) and D(-8,6)
Length CD = √[(-8 - 7)² + (6 - 6)²] = √[(-15)² + 0] = √225 = 15 units
Since it's a square, all sides are equal, so the length of each side is 15 units.
The area of a square is given by the formula side².
Area = 15² = 225 square units
The perimeter of a square is given by the formula 4*side.
Perimeter = 4*15 = 60 units
So, the area of square CDEF is 225 square units and the perimeter is 60 units.
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