Question

What is the total surface area of the square pyramid?

A. 48

B.64

C.76

D.88

Answer 1

option B: 64

Explanation:

surface area of square pyramid, A = a² + 2a√(a²/4 + h²)

where, a = base edge

h = height

as per given in the question,

a = 4

h = 6

by substituting the values in the formula,

A = 4² + 2(4)√(4²/4 + 6²)

= 16 + 8√(16/4 + 36)

= 16 + 8√(4 + 36)

= 16 + 8√40

= 16 + 8(6) = 16 + 48 = 64

thus, total surface are of the square pyramid = 64m²

Answer 2

`\huge\boxed{\sf 64\ m\²}`

Explanation:

In finding surface area of a 3D shape, we need to find the area of all the shapes that figure is made up of.

This square pyramid is made up of:

• 1 square
• 4 triangles

Area of square:

= length × length

= 4 × 4

= 16 m²

Area of triangle:

= 1/2 (base × height)

where base = 4 m, height = 6 m

= 1/2 (4 × 6)

= 2 × 6

= 12 m²

Total surface area:

= Area of 1 square + 4(Area of 1 triangle)

= 16 + 4(12)

= 16 + 48

= 64 m²

`\rule[225]{225}{2}`