The base of a triangle is equal to the perimeter of a square whose diagonal is $6 \sqrt{2}$ 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 3
Diagonal of square = a\(\sqrt {2}\)
Area of right angled triangle = \(\frac{1}{2}\) × Base × Height
Perimeter of square = 4 × side
We know,
a\(\sqrt {2}\)= 6\(\sqrt {2}\)
a = 6 side of square
Perimeter = 4 × 6 = 24 = base of the triangle
Let the height = h
h2 = 144
h = 12
Height of the triangle is equal to side of square
Area of triangle =\(\frac{1}{2}\) × 12× 24 = 144 cm2