Respuesta :
Answer:
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 + ([tex]\frac{1}{2}[/tex] × 15)² = 15² (Pythagoras theorem)
h² = 225 - 7.5² = 168.75
h = [tex]\sqrt{168.75}[/tex] = 12.9904 inches (rounded up to four decimal places)
Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
Area of the four triangular faces is:
([tex]\frac{1}{2}[/tex] × 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
