Answer:
The value are
f = 6 cm
g = 8 cm
Step-by-step explanation:
Given:
ABCE is Trapezium
AD || BC
AD = BC = f
CD = g
Area of ABCE = 60 cm²
Area of ABCD = 48 cm²
To Find :
f = ?
g = ?
Solution:
In the figure ∠ C = 90° and AD || BC
∴ ∠ D = 90° .....Corresponding angles are equal
∴ ABCD is RECTANGLE With Length = f and Breadth = g
∴ [tex]\textrm{Area of Rectangle}=Length\times Breadth\\\textrm{Area of Rectangle}=f\times g\\[/tex]
[tex]\textrm{Area of Triangle AED}= \textrm{Area of Trapezium ABCE}-\textrm{Area of Rectangle ABCD}\\=60-48\\=12\ cm^{2} \\\therefore \textrm{Area of Triangle AED} = \frac{1}{2}\times AD\times DE\\12 =\frac{1}{2}\times f\times 4\\ f=\frac{24}{4}\\\therefore f= 6\ cm[/tex]
Now,
∴ [tex]\textrm{Area of Rectangle}=Length\times Breadth\\\textrm{Area of Rectangle}=f\times g\\[/tex]
[tex]\therefore 48 = f\times g\\48= 6\times g\\\therefore g =\frac{48}{6}\\ g=8\ cm[/tex]
The value are
f = 6 cm
g = 8 cm
