The base of triangle is equal to the perimeter of a square whose diagonal is 9$\sqrt{2}$ cm, and its height is equal to the side of a square whose area is 144$cm^{2}$. The area of the triangle (in $cm^{2}$) is:
Answer & explanation
Correct answer: option 1
We know that,
Diagonal of square = Side\(\sqrt {2}\)
Area of triangle = \(\frac{1}{2}\) × base × height
Perimeter of square = 4 × side
Side \(\sqrt {2}\)= 9\(\sqrt {2}\)
Side = 9
Perimeter = 4 × 9 = 36
24 = base of triangle according to question
Now height is equal to side of square whose area is 144cm2
Height2 = 144
Height = 12
Height of the triangle is equal to side of square = Area of triangle =\(\frac{1}{2}\) × 12× 36 = 216