What is the surface area of the rectangular pyramid?(1 point)

10mcm. 10.6cm. 14cm. 12cm.

1 answer

To find the surface area of a rectangular pyramid, we need to know the dimensions of the base and the slant heights of the triangular faces.

Given:
- Length of base (\( l \)) = 10 cm
- Width of base (\( w \)) = 14 cm
- Height of base (\( h \)) = 12 cm
- Slant height (\( s \)) = 10.6 cm

The surface area (SA) of a rectangular pyramid is the sum of the area of the base and the areas of the four triangular faces.

1. Calculate the area of the base:
\[ \text{Base Area} = l \times w = 10 \, \text{cm} \times 14 \, \text{cm} = 140 \, \text{cm}^2 \]

2. Calculate the area of the four triangular faces:
The area of one triangular face can be calculated using the formula for the area of a triangle:
\[ \text{Area of one triangular face} = \frac{1}{2} \times \text{Base} \times \text{Slant Height} \]

For the two triangles with the base \( l = 10 \) cm:
\[ \text{Area} = 2 \times \left(\frac{1}{2} \times 10 \, \text{cm} \times 10.6 \, \text{cm}\right) = 2 \times 53 \, \text{cm}^2 = 106 \, \text{cm}^2 \]

For the two triangles with the base \( w = 14 \) cm:
\[ \text{Area} = 2 \times \left(\frac{1}{2} \times 14 \, \text{cm} \times 10.6 \, \text{cm}\right) = 2 \times 74.2 \, \text{cm}^2 = 148.4 \, \text{cm}^2 \]

3. Sum the areas:
\[ \text{Total Surface Area} = \text{Base Area} + \text{Area of all triangular faces} \]
\[ \text{Total Surface Area} = 140 \, \text{cm}^2 + 106 \, \text{cm}^2 + 148.4 \, \text{cm}^2 \]
\[ \text{Total Surface Area} = 394.4 \, \text{cm}^2 \]

Therefore, the surface area of the rectangular pyramid is \( 394.4 \, \text{cm}^2 \).