Find the surface area of a square pyramid with side length 5 cm and slant height 4 cm.

h = height

s = slant height

a = side length

P = perimeter of base

e = lateral edge length

r = a/2

V = volume

L = lateral surface area

B = base surface area

A = total surface area

Explanation:

Volume of a square pyramid:

V = (1/3)a2h

Slant Height of a square pyramid:

By the pythagorean theorem we know that

s2 = r2 + h2

since r = a/2

s2 = (1/4)a2 + h2, and

s = √(h2 + (1/4)a2)

This is also the height of a triangle side

Lateral Surface Area of a square pyramid (4 isosceles triangles):

For the isosceles triangle Area = (1/2)Base x Height. Our base is side length a and for this calculation our height for the triangle is slant height s. With 4 sides we need to multiply by 4.

L = 4 x (1/2)as = 2as = 2a√(h2 + (1/4)a2)

Squaring the 2 to get it back inside the radical,

L = a√(a2 + 4h2)

Base Surface Area of a square pyramid (square):

B = a2

Total Surface Area of a square pyramid:

A = L + B = a2 + a√(a2 + 4h2))

A = a(a + √(a2 + 4h2))

i think it is d. e because the next one is igneous.