The perimeter is 32 units, and the area is 39 square units.
How to calculate perimeter and area of a figure
Finding the perimeter and area of the quadrilateral defined by the points (8, -1), (8, 2), (-5, 2), and (-5, -1),
Let's label the points:
A (8, -1)
B (8, 2)
C (-5, 2)
D (-5, -1)
Let's calculate distances for each side using the distance formula
d = √((x₂ - x₁)² + (y₂ - y₁)²)
AB = √{(8 - 8)² + (2 - (-1))²
√(3²)
= 3
BC = √{(-5 - 8)² + (2 - 2)²}
=√{-13²}
= 13
CD = √{(-5 - (-5))² + ((-1) - 2)²}
=√{-3²}
= 3
DA = √{(8 - (-5))² + ((-1) - (-1))²}
=√(13²)
= 13
From the results, the quadrilateral is a rectangle
Calculate the perimeter by adding the side lengths:
Perimeter P= (AB + BC + CD + DA
= 3 + 13 + 3 + 13
= 32 units
Area = Lx W
= 13 x 3
= 39 unit²
So, the perimeter is 32 units, and the area is 39 square units.