Question

question
find the surface area of the figure. round to the nearest hundredths when necessary.
11.2 m
11 m
8 m

Explanation:

Step1: Identify the figure (square pyramid)

The figure is a square pyramid with base side length \( s = 8 \, \text{m} \), slant height (for the triangular faces) needs to be considered, and the base is a square. The surface area of a square pyramid is the sum of the area of the square base and the area of the four triangular faces.

Step2: Calculate the area of the square base

The area of the square base \( B \) is given by \( B = s^2 \), where \( s = 8 \, \text{m} \).

$$ B = 8^2 = 64 \, \text{m}^2 $$

Step3: Calculate the area of one triangular face

Each triangular face has a base of \( 8 \, \text{m} \) and a slant height (the height of the triangular face) of \( 11.2 \, \text{m} \) (from the diagram). The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \).
For one triangular face:

$$ \text{Area of one triangle} = \frac{1}{2} \times 8 \times 11.2 = 44.8 \, \text{m}^2 $$

Step4: Calculate the total area of the four triangular faces

Since there are four identical triangular faces:

$$ \text{Total area of triangles} = 4 \times 44.8 = 179.2 \, \text{m}^2 $$

Step5: Calculate the total surface area

The total surface area \( SA \) is the sum of the base area and the area of the four triangles:

$$ SA = B + \text{Total area of triangles} = 64 + 179.2 = 243.2 \, \text{m}^2 $$

Answer:

The surface area of the square pyramid is \( \boldsymbol{243.2} \) square meters.