Question

find the area of shaded region in the figure


plz answer

Answer 1

☺️ hey mate! here's your answer!☺️

since, BD = 16cm

AD = 12cm

so, by using Pythagoras theorem,

in ∆ABD,

(AD)² + (BD)² = (AB)²

=> (12)² + ( 16)² = (AB)²

=> 144 + 256 = ( AB)²

=> 400 = (AB)²

=> √400 = AB

=> AB = 20cm

then,

total area of shaded region = area of ∆ACB - area of ∆ADB

= { 2(52+48+20) - 2(12+16+20) }cm²

= { 2×120 - 2×48 }cm²

= {240 - 96}cm²

= 144cm² .....answer.

✌️hope it is helpful ✌️!

Answer 2

Area of shaded region = area of ∆ABC - area of ∆ADB.
_____________
$\textbf{Find area of triange ADB:}$

∆ADB is a right angle triangle.

In ∆ADB,
AD = 12 cm
BD = 16 cm

Ar(∆ADB) = 1/2 × base × height

=> Ar(∆ADB) = 1/2 × AD × BD

=> Ar(∆ADB) = 1/2 × 12 × 16

=> Ar(∆ADB) = 96 cm^2
____________________
$\textbf{Find area of triange ABC}$

you can find AB by using Pythagoras theorem.
${AB}^{2} = {AD}^{2} +{ BD}^{2} \\ \\ {AB}^{2} = {12}^{2} + {16}^{2} \\ \\ {AB}^{2} = 144 + 256 = 400 \\ \\ AB = \sqrt{400} \\ \\ AB = 20 \: cm$

The sides of the triangle are 48cm, 52cm and 20cm.

$s = \frac{48 + 52 + 20}{2} = \frac{120}{2} = 60 \: cm$

$\text{Area of triangle ABC} = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{60 \times (60 - 52)(60 - 48)(60 - 20) }$

$= \sqrt{60 \times 8 \times 12 \times 40} \\ \\ = \sqrt{230400} \\ \\ = 480 \: {cm}^{2}$
_______________________

Area of shaded region = area of ∆ABC - area of ∆ADB.

=> Area of shaded region = 480 - 96

=> Area of shaded region = 384 cm^2