https://file.aiquickdraw.com/mathbot/file/17295631065101m4h1ugy.jpg

Let's break down the problem from the image you uploaded, which asks to find the total surface area and volume of a right pyramid with a rectangular base.

### Given:
- **AB = 14 cm** (length of the base)
- **BC = 10 cm** (width of the base)
- **VC = 13 cm** (slant height of the pyramid's side faces)

### (a) **Total Surface Area of the Pyramid**:
To find the total surface area, we need to sum:
1. The area of the rectangular base (ABCD).
2. The areas of the four triangular faces that form the sides of the pyramid.

#### Step 1: Area of the rectangular base
The area of the rectangle is simply:
\[
\text{Area of base} = AB \times BC = 14 \, \text{cm} \times 10 \, \text{cm} = 140 \, \text{cm}^2
\]

#### Step 2: Area of the triangular faces
There are four triangular faces, but two are identical (because the base is a rectangle). Let's calculate their areas.

- The two triangles with base **AB** and slant height **VC**:
  - The area of one of these triangles is:
    \[
    \text{Area of triangle 1} = \frac{1}{2} \times AB \times VC = \frac{1}{2} \times 14 \, \text{cm} \times 13 \, \text{cm} = 91 \, \text{cm}^2
    \]
  - Since there are two of these triangles, their total area is:
    \[
    2 \times 91 = 182 \, \text{cm}^2
    \]

- The two triangles with base **BC** and slant height:
  - We can assume the slant height for these triangles (along the other side) is also 13 cm, although the problem doesn't give it explicitly, it's implied by symmetry.
  - The area of one of these triangles is:
    \[
    \text{Area of triangle 2} = \frac{1}{2} \times BC \times VC = \frac{1}{2} \times 10 \, \text{cm} \times 13 \, \text{cm} = 65 \, \text{cm}^2
    \]
  - Their total area is:
    \[
    2

The figure shows the net of a right pyramid VABCD with a rectangular base. AB = 14 cm, BC = 10 cm, and VC = 13 cm. (a) Find the total surface area of the pyramid. (b) Find the volume of the pyramid. (Give the answers correct to 3 significant figures.)

Solve a right pyramid problem involving a rectangular base with dimensions AB = 14 cm, BC = 10 cm, and slant height VC = 13 cm. Learn how to find the total surface area and volume of the pyramid, using formulas for areas of triangles and rectangles. Suitable for students in Grades 9-11.

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