Answer:
P ≈ 30.73; A = 40.5
Step-by-step explanation:
A. Perimeter
The perimeter of a triangle is the sum of the lengths of the three sides.
P = AB + AT + BT
AT = x₂ - x₁ =5 - (-4) = 5 + 4 = 9
BT = y₂ - y₁ =5 - (-4) = 5 + 4 = 9
To get AB, we must use the Pythagorean Theorem: the square of the hypotenuse equals the sum of the squares of the other two sides.
AB² = AT² + BT² =9² + 9² = 81 + 81
AB² = 162
Take the square root of each side of the equation.
AB = √162 ≈12.73
P = 12.73 + 9 + 9 ≈ 30.73
2. Area
The area of a triangle is one-half the base times the height,
A = ½bh = ½ × AT × BT = ½ × 9 × 9 = 40.5
