Find the area of a right-angled triangle with leg 4 and hypotenuse 5.

As you know, the area of a triangle is equal to half the product of the height and the length of the base to which the height is drawn. In a right triangle, one of the legs is the height, and the other is the base. Therefore, it is necessary to find the length of the second leg according to the Pythagorean law. That is, we write the root of the difference between the squares of the hypotenuse and the known leg:

√ (5 ^ 2 – 4 ^ 2) = √ (25 – 16) = √9 = 3 cm.

Let’s find the area of the figure as:

1/2 * 3 * 4 = 12 * 1/2 = 6 cm ^ 2.

Answer: the area of the figure is 6 cm ^ 2.