Question

please solve this question and its answer is 156cm^2

Answer 1

In ∆ BEC, /_CEB = 90°

By Applying $<b>Pythagoras Theorem</b>$, we get

( BC )² = ( BE )² + ( CE )²

Putting values

( 10 )² = ( BE )² + ( 8 )²

100 = BE² + 64

BE² = 100 - 64

BE² = 36

BE = √36

BE = √ ( 6 × 6 )

BE = 6 cm

Now,

$<u>Area of triangle = 1/2 × Base × Height</u>$

Area = 1/2 × BE × CE

Area = 1/2 × 6 × 8

$<i>Area of triangle = 24 cm²</i>$

In rectangle ABCD,

Length = 18 cm

Breadth = 10 cm

$<u>Area of rectangle = Length × Breadth</u>$

Area = 18 × 10

$<i>Area of rectangle = 180 cm²</i>$

Now,

$<b>Area of shaded region = Area of rectangle - Area of triangle</b>$

= 180 - 24

$<i><u><b>Area of shaded region = 156 cm²</u></i></b>$

Answer 2

Area of rectangle = l×b
=18×10
=180cm^2

In triangle BEC,
By pythagoras theorem,
Bc^2= EC^2 +EB^2
10^2=8^8 +EB^2
100 - 64 =EB^2
36=EB^2
EB = √36
EB = 6cm.

Area of triangle BEC
= 1/2 × b×h
=1/2 ×6 ×8
=24cm^2

Area of shaded region
=Area of rectangle - Area of triangl
=180-24
=156cm^2