Which expression represents the surface area of the pyramid?

Steps to Solve

1. Identify the base area of the pyramid The base of the square-based pyramid has dimensions $10 \times 10$. Thus, the area of the base can be calculated as: $$ \text{Base Area} = 10 \cdot 10 = 100 $$

2. Calculate the area of the triangular faces The pyramid has four triangular faces. Each triangular face has a base of 10 and height of 8. The area $A$ of one triangle can be calculated using the formula: $$ A = \frac{1}{2} \times \text{base} \times \text{height} $$ Substituting in the values: $$ A = \frac{1}{2} \times 10 \times 8 = 40 $$

3. Determine the total surface area Since there are four triangular faces, the total area of the triangular faces can be calculated as: $$ \text{Total triangular faces area} = 4 \times 40 = 160 $$

Now, add the base area to the total area of the triangular faces: $$ \text{Surface Area} = \text{Base Area} + \text{Total triangular faces area} $$ $$ \text{Surface Area} = 100 + 160 = 260 $$

4. Identify the correct expression Now you can evaluate which of the provided options corresponds to the total surface area calculated:

• Option A: $100 + 40 + 40 + 40 + 40$ (equivalent to $100 + 160$)
• Option B: $10 \cdot 8$ (area of one triangle, not the entire surface area)
• Option C: $40 \cdot 4$ (is the area of triangles only)
• Option D: $100 + 80 + 80 + 80 + 80$ (not correct for the given pyramid)

Option A represents the correct expression for the surface area of the pyramid.