Question

find the area of shaded region.
(ABC)
BC=48cm
AC=52cm
​

Answer 1

Answer:

Area of shaded region is $312.25cm^{2}$

Step-by-step explanation:

First we have to find the length of the third side of the larger triangle using pythagoras theorem ($a^{2} + b^{2} = c^{2}$).

So the 3rd side would be, $c = \sqrt{10^2 + 12^2}$ = 15.62

Therefore the area of the larger triangle according to Heron's theorem($\sqrt{s(s-a)(s-b)(s-c)}$ where $s = \frac{a+b+c}{2}$ will be :-

$s = \frac{48 + 52+15.6}{2} =57.8$

$Area = \sqrt{57.8 * 9.8*5.8*42.2} = 372.35cm^{2$

Area of smaller triangle = $\frac{1}{2} * base * height$

$a = \frac{1}{2} * 10 * 12 = 60cm^{2}$

Therefore shaded area $= 372.35-60 = 312.25cm^2$