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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 cm2. The area of the triangle (in cm2) is:

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 cm2. The area of the triangle (in cm2) is: Correct Answer 144

Given:

Base of triangle is equal to the perimeter of square whose diagonal if 6√ 2

Formula used : diagonal of square = a√ 2

Area of triangle = 1/2 base × height 

Perimeter of square = 4 × side 

calculation 

a√ 2= 6√ 2 

a= 6 side of square 

4× 6 = 24

24 = base of triangle according to question

now height is equal to side of square whose area is 144cm2 

b2 = 144

b= 12

⇒ height of the triangle is equal to side of square

⇒ Area of triangle =1/2× 12× 24

⇒ Area of triangle= 144 cm2

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