Question

find the area of shaded region​

Answer 1

In ∆ADB
as angle D is 90°

•°• by using Pythagoras Theorem
H² = P²+ B²
AB² = AD² + BD²
= (12)² + (5)²
= 144 + 25
= 169
AB = √169 = 13

Now In ∆ ABC
By using Herons formula

s=13+14+15 / 2 = 42/2 = 21


area of ∆ ABC = √s(s-a)(s-b)(s-c)
= √21(21-13)(21-14)(21-15)
= √21×8×7×6
= √7×3×2×2×2×7×2×3
= 7×2×3×2
= 84 sq units

Now In ∆ADB
by using Herons formula

s = 12+5+13 /2 = 30/2 = 15


area of ∆ ADB = √15(15-12)(15-5)(15-13)
= √15×3×10×2
= √5×3×3×5×2×2
= 5×3×2
=30 sq units
so area of shaded region = 84-30 = 54 sq units

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hope this helps u.....