Question

A pyramid.Short description, A pyramid.,Long description,
The surface area, A, of a pyramid can be found by using the formula A equals one half P times S plus B, where P is the perimeter of the base, S is the slant height of the pyramid, and B is the area of the base of the pyramid. The pyramid shown has a square base.

One side of the base of the pyramid is 10 feet, the slant height is 13 feet, and the height from the top of the pyramid to the bottom is 12 feet. The slant height, part of the base, and the vertical height form a right triangle inside the pyramid.


Question
What is the total surface area of the pyramid in square feet?

Answer options with 5 options
A.
230

B.
300

C.
340

D.
360

E.
750

Answer 1

To find the total surface area of the pyramid, we can use the given formula:

\[ A = \frac{1}{2} P S + B \]

Where:
- \( P \) is the perimeter of the base,
- \( S \) is the slant height,
- \( B \) is the area of the base.

### Step 1: Calculate the Perimeter of the Base (\( P \))
Since the base is a square, the perimeter \( P \) can be calculated as:

\[ P = 4 \times \text{side length} \]
\[ P = 4 \times 10 \text{ feet} = 40 \text{ feet} \]

### Step 2: Calculate the Area of the Base (\( B \))
The area of the base \( B \) for a square is:

\[ B = \text{side length}^2 \]
\[ B = 10^2 = 100 \text{ square feet} \]

### Step 3: Slant Height (\( S \))
The slant height is given as:

\[ S = 13 \text{ feet} \]

### Step 4: Substitute values into the surface area formula
Now we can plug these values into the surface area formula:

\[ A = \frac{1}{2} (P \times S) + B \]
\[ A = \frac{1}{2} (40 \text{ feet} \times 13 \text{ feet}) + 100 \text{ square feet} \]
\[ A = \frac{1}{2} (520) + 100 \]
\[ A = 260 + 100 \]
\[ A = 360 \text{ square feet} \]

### Final Answer
The total surface area of the pyramid is:

**D. 360 square feet**