Answer
Perimeter = 20.9 units
Area = 16.0 square units
Step-by-step explanation
We are asked to find the perimeter and the area of the triangle given.
The perimeter of a figure is the sum of all its exterior dimensions. So, to do this, we need to find the length of each side of this triangle.
AB, AC and BC
The distance between two points with the coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
For AB
(x₁, y₁) and (x₂, y₂) is A (0, 9) and B (4, 9) respectively
x₁ = 0
y₁ = 9
x₂ = 4
y₂ = 9
AB = √[(4 - 0)² + (9 - 9)²]
AB = √[(4)² + (0)²]
AB = √(16)
AB = 4 units
For AC
(x₁, y₁) and (x₂, y₂) is A (0, 9) and C (0, 1) respectively
x₁ = 0
y₁ = 9
x₂ = 0
y₂ = 1
AC = √[(0 - 0)² + (1 - 9)²]
AC = √[(0)² + (-8)²]
AC = √(64)
AC = 8 units
For BC
(x₁, y₁) and (x₂, y₂) is B (4, 9) and C (0, 1) respectively
x₁ = 4
y₁ = 9
x₂ = 0
y₂ = 1
BC = √[(0 - 4)² + (1 - 9)²]
BC = √[(-4)² + (-8)²]
BC = √(16 + 64)
BC = √80
BC = 8.94 units
Perimeter of ABC = AB + AC + BC
= 4 + 8 + 8.94
= 20.94
= 20.9 units to the nearest tenth
The area of a triangle is given as
Area = ½ × Base × Height
Base = AB = 4 units
Height = AC = 8 units
Area = ½ × 4 × 8
Area = 16.0 square units.
Hope this Helps!!!