Question

A composite figure is formed by a parallelogram
A
B
C
D
𝐴
𝐵
𝐶
𝐷
and a rhombus
C
D
E
F
𝐶
𝐷
𝐸
𝐹
(where
C
D
𝐶
𝐷
is a shared side). The two figures are adjacent, with the rhombus positioned to the "right" of the parallelogram along the shared side
C
D
𝐶
𝐷
.
In parallelogram
A
B
C
D
𝐴
𝐵
𝐶
𝐷
, side
B
C
𝐵
𝐶
has a length of 25 units, and the perpendicular height from
B
C
𝐵
𝐶
to the opposite side
A
D
𝐴
𝐷
is 20 units. The length of the diagonal
B
D
𝐵
𝐷
is 30 units.
The rhombus
C
D
E
F
𝐶
𝐷
𝐸
𝐹
shares the side
C
D
𝐶
𝐷
with the parallelogram. All sides of a rhombus are equal in length, so each side of
C
D
E
F
𝐶
𝐷
𝐸
𝐹
is the same length as
C
D
𝐶
𝐷
.
One of the diagonals of the rhombus,
D
F
𝐷
𝐹
, has a length of 48 units.
The Challenge:
Calculate the length of the other diagonal of the rhombus,
C
E
𝐶
𝐸
.
Determine the total area of the composite figure
Design a figure for this problem