Question

ABCE is a trapet AD is parallel to BC DE=4cm area of ABCE=60cm?area of ABCD=48cm work out the values of f and g show all your working please be quick thank youuuu

Answer 1

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

∴ $\textrm{Area of Rectangle}=Length\times Breadth\\\textrm{Area of Rectangle}=f\times g$

$\textrm{Area of Triangle AED}= \textrm{Area of Trapezium ABCE}-\textrm{Area of Rectangle ABCD}\\=60-48\\=12\ cm^{2} \\\therefore \textrm{Area of Triangle AED} = \frac{1}{2}\times AD\times DE\\12 =\frac{1}{2}\times f\times 4\\ f=\frac{24}{4}\\\therefore f= 6\ cm$

Now,

∴ $\textrm{Area of Rectangle}=Length\times Breadth\\\textrm{Area of Rectangle}=f\times g$

$\therefore 48 = f\times g\\48= 6\times g\\\therefore g =\frac{48}{6}\\ g=8\ cm$

The value are

f = 6 cm

g = 8 cm