Question

find the area of shaded region plzzz faster

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

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

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$\huge{\bold{\textsf{\pink{Find\:the\:Area\:of\:Triangle\:ADB:}}}}$

∆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

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$\huge{\bold{\textsf{\pink{Find\:Area\:of\:Triangle\:ABC:}}}}$

You can find AB by using Pythagoras theorem.

$AB^{2}=AD^{2}+BD^{2}$

$AB^{2}=12^{2}+16^{2}$

$AB^{2}=144+256=400$

$AB=20cm$

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

$s=\frac{48+5+20}{2}=\frac{120}{2}=60cm$

$Area\:of\:the\:Triangle\:ABC=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{60\:\times\:(60-52)(60-48)(60-20)}$

$=\sqrt{60\:\times\:8\:\times\:12\:\times\:40}$

$=\sqrt{230400}$

$=480cm^{2}$

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

=> Area of shaded region = 480 - 96

=> Area of shaded region = 384 cm^2