Find the area of the shaded region
Please Answer according to Class 9 Herons Formula
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Find the area of the shaded region
Please Answer according to Class 9 Herons Formula
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Verified answer
Step-by-step explanation:
Given:
In the right-angled triangle ADB, the right angle at D
In the triangle ABC, we have
To find:
Area of the shaded portion (ADBC)
Steps to get the answer,
So,
In triangle ADB, (Using Pythagoras Theorem)
⇒ (AD)² + (BD)² = (AB)²
⇒ (12)² + (16)² = (AB)²
⇒ 144 + 256 = (AB)²
⇒ 400 = (AB)²
⇒ 20 = AB
[Taking square roots both the sides]
So, the value of AB = 20 cm
Now,
We have sides of triangle ABC
S = Perimeter ÷ 2
S = (20+48+52) ÷ 2
S = 120 ÷ 2
S = 60
[tex]= \sqrt{S(S-a)(S-b)(S-c)}[/tex] units sq.
[tex]= \sqrt{60(60-20)(60-48)(60-52)}[/tex]
[tex]= \sqrt{60(40)(12)(8)}[/tex]
[tex]= \sqrt{\underline{2*2}*3*5*(\underline{2*2}*2*5)(\underline{2*2}*3)(\underline{2*2}*2)}[/tex]
[tex]= 2*2*2*2\sqrt{3*5*(2*5)*(3)*(2)}[/tex]
[tex]= 16\sqrt{\underline{3*3} *\underline{5*5}* \underline{2*2}}[/tex]
= 16 * 3 * 5 * 2
= 480 cm sq.
Now,
Area of the right-angled triangle ADB
= 1/2 * base * height
= 1/2 * 12 * 16
= 6 * 16
= 96 cm sq.
Now,
Area of shaded region = 480 - 96
Area of shaded region = 384 cm sq.
REFER TO THE ATTACHMENTS
HOPE IT HELPS :)