Question

Find surface area of a square pyramid with “a” of .5cm and “l” of .8cm. (units needed)

Answer 1

To find the surface area of a square pyramid, you need to consider both the base area and the lateral (triangular) surface area.

1. **Base Area**: For a square pyramid, the base area \(A_{base}\) is given by:
\[
A_{base} = a^2
\]
where \(a\) is the length of one side of the base.

2. **Lateral Surface Area**: The lateral surface area \(A_{lateral}\) consists of 4 triangular faces. The area of one triangular face is given by:
\[
A_{triangle} = \frac{1}{2} \times a \times l
\]
where \(l\) is the slant height. Since there are 4 triangular faces:
\[
A_{lateral} = 4 \times A_{triangle} = 4 \times \left(\frac{1}{2} \times a \times l\right) = 2 \times a \times l
\]

3. **Total Surface Area**: The total surface area \(A_{total}\) is the sum of the base area and the lateral surface area:
\[
A_{total} = A_{base} + A_{lateral}
\]
\[
A_{total} = a^2 + 2 \times a \times l
\]

Now, plug in the values of \(a = 0.5\) cm and \(l = 0.8\) cm:

1. Calculate the base area:
\[
A_{base} = (0.5 \, \text{cm})^2 = 0.25 \, \text{cm}^2
\]

2. Calculate the lateral surface area:
\[
A_{lateral} = 2 \times (0.5 \, \text{cm}) \times (0.8 \, \text{cm}) = 2 \times 0.4 \, \text{cm}^2 = 0.8 \, \text{cm}^2
\]

3. Combine both areas to find the total surface area:
\[
A_{total} = 0.25 \, \text{cm}^2 + 0.8 \, \text{cm}^2 = 1.05 \, \text{cm}^2
\]

Thus, the total surface area of the square pyramid is \( \boxed{1.05 \, \text{cm}^2} \).