Question

find the area of the shaded part.
5
cdef is
a rectangle
with an area
of 24 ft².
a =
6
a =

Explanation:

Step1: Find the length of \( FE \)

The area of rectangle \( CDEF \) is \( A = CD\times FE \). Given \( A = 24\space ft^{2} \) and \( CD = 6\space ft \), then \( FE=\frac{A}{CD}=\frac{24}{6}=4\space ft \).

Step2: Analyze the area relationship

The area of the shaded triangle: The base of the shaded triangle is \( CF \) (where \( CF = 3\space ft \)) and the base of the large triangle (with base \( CE=CF + FE=3 + 4=7\space ft \)) and the shaded triangle and the large triangle (formed by the diagonal of the rectangle) have the same height.
Another way: The area of \( \triangle CDF=\frac{1}{2}\times CD\times CF=\frac{1}{2}\times6\times3 = 9\space ft^{2}\)

Answer:

\(9\space ft^{2}\)