In the given figure ABC and DBC have the same base BC such that AB = 120m, AC = 122m, BC = 22m, BD = 24m and CD = 26m. Find the area of the shaded region. (Take = 10.25)

Question

Philoid · Accepted Answer

It is given in the question that,

AB = 120 m

AC = 122 m

BC = 22 m

BD = 24 m

And, CD = 26 m

We know that,

Perimeter of triangle = Sum of all sides

∴ Perimeter of = AB + BC + AC

= 120 + 22 + 122

= 264 m

s =

=

= 132 m

Now, Area () =

=

= 11 × 12 × 10

= 1320 m²

Now, in

BC = a, BD = b and CD = c

∴ Perimeter of = 22 + 24 + 26

= 72 m

s =

=

= 36 m

Hence, area ( =

=

= 24 × 10.25

= 246 m²

∴ Area of shaded region = Area () – Area ()

= 1320 – 246

= 1074 m²