Question

The area of the shaded region in the given triangular figure is $52$ square units. What is the height of the larger triangle?

Answer 1

Given: Area of the shaded region $=52$ square units

Let the height of the smaller triangle be ${}^{\prime }{h}^{\prime }$.

Height of the larger triangle $=6+h$

Area of the shaded region of the triangle $=$ Area of larger triangle $-$ Area of smaller triangle.

Area of shaded region $=\frac{1}{2}\times 12\times (6+h)-\frac{1}{2}\times 8\times h$

$\therefore 52=\frac{1}{2}\times 12\times (6+h)-\frac{1}{2}\times 8\times h$

$\Rightarrow 52=36+6h-4h$
$\Rightarrow 52-36=2h$
$\Rightarrow 2h=16$
$\Rightarrow h=8$

Height of the larger triangle $=6+6=8+6=14$ units