Madhya Pradesh Police Exam Model Paper 5

Given:
Diagonal of a square $=9\sqrt{2}\mathit{c}\mathit{m}$
Area of a square $=144\mathit{c}{\mathit{m}}^2$
Formula used:
Area of a triangle = 1/2 × base × height
Perimeter of a square $=4\mathit{a}$
Area of a square $={\mathit{a}}^2$
Here, a = side of a square
Calculation:
We know that diagonal of a square $=\mathit{a}\sqrt{2}$
$\mathit{a}\sqrt{2}=9\sqrt{2}$
⇒ a = 9
Perimeter of the square = 4 × 9 = 36 cm = base of the triangle
Area of the square = 144 cm^2
$\Rightarrow {\mathit{a}}^2=144\mathit{c}{\mathit{m}}^2$
⇒ a = 12 cm = height of the triangle
Area of the triangle $=1/2\times 36\times 12$
$\Rightarrow 18\times 12=216$
∴ Area of the triangle is 216