Question

there are two triangular faces one measures a height of 15 base of 10 and the other with the height of 12 base of 8. What is the surface area of the rectangular pyramid? (1 point) mm2

Answer 1

To calculate the surface area of a rectangular pyramid with two triangular faces, we need to determine the areas of these triangular faces and then add them to the area of the rectangular base.

1. **Calculate the area of the first triangular face:**
Given:
- Height (h₁) = 15 mm
- Base (b₁) = 10 mm

The area (A₁) of a triangle is given by the formula:
\[
A₁ = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times b₁ \times h₁
\]
\[
A₁ = \frac{1}{2} \times 10 \times 15 = 75 \, \text{mm}^2
\]

2. **Calculate the area of the second triangular face:**
Given:
- Height (h₂) = 12 mm
- Base (b₂) = 8 mm

The area (A₂) of the second triangular face is calculated similarly:
\[
A₂ = \frac{1}{2} \times b₂ \times h₂
\]
\[
A₂ = \frac{1}{2} \times 8 \times 12 = 48 \, \text{mm}^2
\]

3. **Calculate the area of the base:**
For a rectangular pyramid, if not specified, we can assume a rectangular base formed by the bases of the two triangular faces. Here, assume the base's dimensions (length and width) correspond to the base lengths of the triangles. We can define the base as 10 mm by 8 mm.

The area (A_base) of the rectangular base is:
\[
A_{base} = 10 \times 8 = 80 \, \text{mm}^2
\]

4. **Calculate the total surface area of the pyramid:**
Now, add the areas of the triangular faces and the base:
\[
\text{Total Surface Area} = A₁ + A₂ + A_{base}
\]
\[
\text{Total Surface Area} = 75 + 48 + 80 = 203 \, \text{mm}^2
\]

Therefore, the surface area of the rectangular pyramid is **203 mm²**.