Answer:
Area of Pyramid = 192.96 in.²
Step-by-step explanation:
Given: Square base pyramid.
side of square = 8 in.
Height of pyramid = 7 in.
To find: Total Surface Area of Pyramid
Figure is attached.
Side triangles are all equal in area as they equal length of base and height.
Thus,
Total Surface area of pyramid = area of square base + area of 4 equal
side triangles.
from figure,
In Δ ABC,
using Pythagoras theorem
AC² = AB² + CB²
AC² = 7² + 4²
AC² = 49 + 16
AC² = 65
AC = √65 in.
AC = 8.06 in.
Base of Triangles = 8 in.
Height of triangles = 8.06 in.
[tex]\implies\:Area\:of\;Triangle\,=\,\frac{1}{2}\times base\times height[/tex]
[tex]=\,\frac{1}{2}\times8\times8.06[/tex]
= 4 × 8.06
= 32.24 in.²
Area of Square base = side × side
= 8 × 8
= 64 in.²
⇒ Area of Pyramid = Area of Square base + 4 × Area of triangle
= 64 + 4 × 32.24
= 64 + 128.96
= 192.96 in.²
Therefore, Area of Pyramid = 192.96 in.²
