The sides of the base of a regular quadrangular pyramid are 24, the side edges are 13.

The sides of the base of a regular quadrangular pyramid are 24, the side edges are 13. Find the surface area of this pyramid.

Since the pyramid is regular, there is a square at its base, and its lateral faces are isosceles triangles.

In an isosceles triangle PCD, we construct the height of the PH, which is also its median, then DH = CH = CD / 2 = 24/2 = 12 cm.

In a right-angled triangle PDH, according to the Pythagorean theorem, PH ^ 2 = PD ^ 2 – DH ^ 2 = 169 – 144 = 25.

DН = 5 cm.

Determine the area of ​​the base of the pyramid. Sbn = АD ^ 2 = 24 * 24 = 576 cm2.

Determine the area of ​​the triangle PCD. Sрсд = СD * РН / 2 = 24 * 5/2 = 60 cm2.

Determine the surface area of ​​the pyramid.

Sпов = Sсн + 4 * Sрсд = 576 + 4 * 60 = 816 cm2.

Answer: The area of ​​the pyramid is 816 cm2.