Question

FIND THE AREA OF THE SHADED REGION IN THE FIGURE GIVEN.... :-

Answer 1

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Answer 2

Answer:

384 cm².

Step-by-step explanation:

Pythagoras theorem:

$hypotenuse^2=base^2+perpendicular^2$

Use Pythagoras theorem in triangle ADB,

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

$AB^2=(12)^2+(16)^2$

$AB^2=144+256$

$AB^2=400$

Taking square root on both sides.

$AB=20$

The area of a right angled triangle is

$A=\frac{1}{2}\times base\times height$

Area of triangle ABD,

$A=\frac{1}{2}\times (16)\times (12)=96$

The area of triangle ABD is 96 cm².

If a,b and c are three sides of a triangle, then the area of triangle is

$A=\sqrt{s(s-a)(s-b)(s-c)}$

where,

$s=\frac{a+b+c}{2}$

In triangle ABC the measure of three sides are 20cm, 48 cm and 52 cm.

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

The area of triangle ABC is

$A=\sqrt{60(60-20)(60-46)(60-52)}$

$A=\sqrt{268800}$

$A=480$

The area of triangle ABC is 480 cm².

The area of shaded region is

$480-96=384$

Therefore, the area of shaded region is 384 cm².