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

96 units²

Step-by-step 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

2623.6144m²

Step-by-step 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