Answer :
Explanation :
The area of the shaded region would be equal to the area of triangle ABC - the area of triangle ABD
given to us that ΔABD = right angled triangle
thus, we can find the measure of AB using the pythagoras theorem,
- AB = √[(BD)^2 + (AD)^2)]
- AB = √[(16cm)^2 + (12cm)^2]
- AB = √(256cm^2 + 144cm^2)
- AB = √(400cm^2)
- AB = 20cm
now, since we have the measure of AB, we can further continue to find the area of the respective triangles using the herons formula
- Area = √[s(s-a)(s-b)(s-c)]
wherein ,
- s = semi perimeter
- perimeter = sum of all the three sides
In ΔABC,
- s = (20cm + 48cm + 52cm)/2
- s = 60cm
- Area = √[60cm(60cm -20cm)(60cm-48cm)(60cm-52cm)]
- Area = √(60cm*40cm*12cm*8cm)
- Area = √(230,400cm^4)
- Area = 480cm^2
In ΔABD,
- s = (20cm + 16cm + 12cm)/2
- s = 48cm/2
- s = 24cm
- Area = √[24cm(24cm-20cm)(24cm-16cm)(24cm-12cm)]
- Area = √(24cm*4cm*8cm*12cm)
- Area = √(9,612cm^4)
- Area = 96cm^2
thus, the area of the shaded region would be
- the area of triangle ABC - the area of triangle ABD
- 480cm^2 - 96cm^ 2 = 384cm^2
therefore,the required answer is 384cm^2 .
