Question

If w = 6 units, x = 3 units, and y = 5 units, what is the surface area of the figure?

Answer 1

*see attachment for the diagram

Answer:

A. 178 units²

Step-by-step explanation:

Surface area of the figure = (surface area of the square pyramid + surface area of the square prism) - 2(base area of the square pyramid)

✔️Surface area of the square pyramid = s² + 2*s*l

Where,

s = side length of square base (w) = 6 units

l = slant height = ?

Use Pythagorean theorem to find l

l = √((w/2)² + y²)

l = √((6/2)² + 5²) = √(9 + 25)

l = √34

l ≈ 5.8 units

Surface area of the square pyramid = 6² + 2*6*5.8 = 105.6 units²

✔️Surface area of square prism:

SA = 2a² + 4ah

Where,

a = w = 6 units

h = x = 3 units

Substitute

SA = 2(6²) + 4*6*3

= 72 + 72

= 144 units²

✔️base area of the square pyramid = s²

s = w

Base area = 6²

Base area = 36 units²

✅Surface area of the figure = (surface area of the square pyramid + surface area of the square prism) - 2(base area of the square pyramid)

Surface area of the figure = (105.6 + 144) - 2(36)

= 249.6 - 72

= 177.6

≈ 178 units²