Answer:
- height: √51.2 units
- base: √80 units
- area 64 units²
Step-by-step explanation:
a) height: The length AP is √(3.2² +6.4²) = √51.2 units.
b) base length: The length CD is √(8²+4²) = √80 units.
c) The area is the product of the base and height:
A = bh = √(80·51.2) = √4096 = 64 . . . . square units.
_____
Comment on this problem
The area of this rhombus is much more easily found using the diagonals. The area of a rhombus is half the product of the lengths of the diagonals. Since those are aligned with the axes, their lengths are easily found as ...
AC = 16
BD = 8
Area = (1/2)AC·BD = (1/2)(16)(8) = 64 . . . square units
Obviously, the problem is not about the area of the rhombus. Rather, it is about finding the lengths of line segments from their coordinates.
