Answer:
A = 480 mm²
Step-by-step explanation:
the area (A) of a rhombus is calculated as
A = [tex]\frac{1}{2}[/tex] product of diagonals
The diagonals are perpendicular bisectors of each other , so
Δ XVW is a right triangle
using Pythagoras' identity in the right triangle , then
XV² + WV² = WX²
XV² + 24² = 26²
XV² + 576 = 676 ( subtract 576 from both sides )
XV² = 100 ( take square root of both sides )
XV = [tex]\sqrt{100}[/tex] = 10
then
XZ = 2 × XV = 2 × 10 = 20
and
WY = 2 × WV = 2 × 24 = 48
A = [tex]\frac{1}{2}[/tex] × XZ × WY = [tex]\frac{1}{2}[/tex] × 20 × 48 = 10 × 48 = 480 mm²
