Question

Find the surface area of the right square pyramid. Round your answer to the nearest hundredth.

Answer 1

A= a^2+2a\square root{\frac{a^2}{4}}+h^2
a=base=8
h=height=7
A=surface area
A=177

Answer 2

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.

$\implies\:Area\:of\;Triangle\,=\,\frac{1}{2}\times base\times height$

                                       $=\,\frac{1}{2}\times8\times8.06$

                                       = 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