Find the area of a right-angled triangle if its hypotenuse is √52, and one of the legs is 6.

According to the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse.

Let the second leg be x cm.

Let’s use the formula, compose and solve the equation:

x ^ 2 + 6 ^ 2 = (√52) ^ 2,

x ^ 2 + 36 = 52,

x ^ 2 = 16,

x = 4 cm.

The area of a right-angled triangle is half the product of its legs:

1/2 * 4 * 6 = 12 cm2.

Answer: the area of a right-angled triangle is 12 cm2.