Question

Бічна грань правильної трикутної піраміди е прямокутним трикутником з гіпо-тенузою 6 см. Визначте площу (у см?) бічної поверхні цієї піраміди.

Answer 1

Calculating the Surface Area of a Right Triangular Pyramid

To calculate the surface area of a right triangular pyramid, we can use the formula:

Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height

Given that the right triangular pyramid has a right-angled triangle as its lateral face with a hypotenuse of 6 cm, we can proceed with the calculation.

Calculating the Base Area

The base of the right triangular pyramid is a right-angled triangle. To find the area of the base, we can use the formula for the area of a triangle:

Base Area = (1/2) * Base * Height

Calculating the Perimeter of the Base

The perimeter of the base of the right triangular pyramid can be found by adding the lengths of its three sides.

Calculating the Slant Height

The slant height of the right triangular pyramid can be found using the Pythagorean theorem, as the hypotenuse of the right-angled triangle is given.

Now, let's calculate the surface area of the right triangular pyramid using the given information.