Question

Find the total surface area of the following pyramids: A regular square pyramid has a height of 4 and a base with area 36.

Answer 1

2623.6144m²

Explanation:

Total Surface Area of a Square Pyramid

a * (a + √(a² + 4h²))

where,

a = area of base

h = height

Using the formula above

a * (a + √(a² + 4h²))

data given :

a = 36

h = 4

a * (a + √(a² + 4h²))

T.S.A. = a * (a + √(a² + 4h²))

Inputting values

T.S.A. = 36 * (36 + √(36² + 4 * 4²))

T.S.A. = 36 * (36 + √(36² + 4 * 16))

T.S.A. = 36 * (36 + √(36² + 64))

T.S.A. = 36 * (36 + √(1296 + 64))

T.S.A. = 36 * (36 + √(1360))

T.S.A. = 36 * (36 + 36.87817782917154)

T.S.A. = 36 * (72.87817782917154)

T.S.A. = 36 * 72.8782

T.S.A. = 2623.614401850175

Therefore Total Surface Area (T.S.A.) is 2623.6144m²

Answer 2

96 units²

Explanation:

Base area = side² = 36

Each side = 6 units

Surface area includes 1 square and 4 identical slant triangles

Area of square: 36

height of a slant triangle:

height² = 3² + 4² = 25

height = 5

Area of each slant triangle = ½×6×5 = 15

Total SA = 36 + 4(15)

= 36 + 60 = 96 units²