Question

in figure find the area of shaded region
[use underoot 35=5.9]​

Answer 1

Answer:

50.8sq cm

Step-by-step explanation:

Triangle BCD is a right angle triangle.

Area of triangle BCD=(1/2) ×12×5=30sq cm.

BC=√(12^2+5^2) =13

Now Area of triangle ABC is determined by hero's formula.

Area of triangle ABC is 70.8sq cm.

Therefore area of the shaded region=(70.8-30) =50.8sq cm

Answer 2

Given :

BD = 12 cm

CD = 5 cm

AB = 18 cm

AC = 11 cm

To Find : Area of shaded region

Solution:

In Triangle BDC

Perpendicular = BD = 12 cm

Base = CD = 5 cm

Area of triangle BDC =$\frac{1}{2} \times 12 \times 5 =30 sq.cm.$

To Find hypotenuse we will use Pythagoras theorem :

$Hypotenuse^2 = Perpendicular^2+Base^2\\Hypotenuse^2 = 12^2+5^2\\Hypotenuse = \sqrt{12^2+5^2}$

Hypotenuse = 13

So, BC = 13 cm

In triangle ABC

AB = 18 cm

AC = 11 cm

BC = 13 cm

To find area we will use heron's formula :

$A=\sqrt{s(s-a)(s-b)(s-c)}\\s=\frac{a+b+c}{2}\\s=\frac{18+11+13}{2}\\s=21\\A=\sqrt{21(21-18)(21-11)(21-13)}\\A=12\sqrt{35}\\A=12 \times 5.9=70.8$

So, Area of triangle ABC is 70.8 sq.cm.

Area of shaded region  = Area of triangle ABC - Area of triangle BDC = 70.8 - 30= 40.8 sq.cm.

Hence area of shaded region is 40.8 sq.cm.