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

Area of Pyramid = 192.96 in.²

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\,=\,(1)/(2)* base* height`

`=\,(1)/(2)*8*8.06`

= 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