Answer:
- Perimeter: 16.1 cm
- Area: 12 cm²
Explanation:
You want the perimeter and area of the triangle shown.
Perimeter
The perimeter is the sum of the lengths of the sides of the triangle. For sides not vertical or horizontal, the distance formula can be used to find the side length.
d = √((x2 -x1)² +(y2 -y1)²)
AC = √((-4 -0)² +(0 -4)²) = 4√(1+1) = 4√2 ≈ 5.657 . . . . cm
AB = √((2 -0)² +(0 -4)²) = 2√(1 +4) = 2√5 ≈ 4.472 . . . . cm
Then the perimeter is ...
AC +AB +CB = 5.657 +4.472 +6 = 16.129 ≈ 16.1 . . . . cm
The perimeter is 16.1 cm.
Area
The area is half the product of the base and height. The base is AC, length 6. The height is AO, length 4.
A = 1/2(6)(4) = 12 . . . . cm²
The area is 12 cm².
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