Find the total surface area of the triangular pyramid in square inches, each side is 15 inches

623.7120 square inches (rounded up to four decimal places)

Step-by-step explanation:

Given; each side of the triangular pyramid is 15 inches.

The base therefore is a square measuring 15 inches by 15 inches

The area of the base is length² = (15 inches)² = 225 square inches

The other four faces are triangular shapes that meet at the top of the pyramid.

To find the area of each triangular shape;

We first need to find the height(h) of each triangular shape.

h² + ( × 15)² = 15² (Pythagoras theorem)

h² = 225 - 7.5² = 168.75

h = = 12.9904 inches (rounded up to four decimal places)

Area of a triangle = × base × height

Area of the four triangular faces is:

(  × 15 × 12.9904) × 4 = 398.7120 square inches

Total surface area of the pyramid = Area of the base + total area of the four triangular faces

Surface area of the pyramid = 225 square inches + 398.7120 square inches = 623.7120 square inches