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 \( CF \)

Since the area of rectangle \( CDEF \) is \( A = CD\times CF \), and \( A = 24\space ft^{2}\), \( CD=6\space ft \). Then \( CF=\frac{A}{CD}=\frac{24}{6} = 4\space ft \)

Step2: Calculate the area of the shaded triangle

The base of the shaded triangle is \( CF - 3=4 - 3=1\space ft \), and the base of the large - triangle (with the same height) is \( CD = 6\space ft \).
The area of a triangle is \( A=\frac{1}{2}\times base\times height \). Here, the height of the shaded triangle is the same as the height of the triangle with base \( CD \) (parallel sides property).
The area of the shaded triangle \( A=\frac{1}{2}\times(4 - 3)\times6=3\space ft^{2} \)

Answer:

\(3\space ft^{2}\)