Question

What is the surface area of a rectangular pyramid with a base of 14 cm a side height of 10 cm a length of 12 cm and another side height of 10.6 cm

Answer 1

To find the surface area of a rectangular pyramid, we need to calculate the area of the base and the area of the four triangular faces.

1. Area of the base:
The base of the rectangular pyramid is a rectangle with dimensions 14 cm by 12 cm. The area of the base is given by:
base area = length x width
base area = 14 cm x 12 cm
base area = 168 cm^2

2. Area of the triangular faces:
The two side faces have a height of 10 cm, and the other two side faces have a height of 10.6 cm. The area of each triangular face is given by:
triangular face area = 0.5 x base x height

For the triangular faces with a height of 10 cm:
triangular face area = 0.5 x 14 cm x 10 cm
triangular face area = 70 cm^2

For the triangular faces with a height of 10.6 cm:
triangular face area = 0.5 x 12 cm x 10.6 cm
triangular face area = 63.6 cm^2

3. Total surface area:
The total surface area of the rectangular pyramid is the sum of the base area and the areas of the four triangular faces:
total surface area = base area + 2 x triangular face area (with a height of 10 cm) + 2 x triangular face area (with a height of 10.6 cm)
total surface area = 168 cm^2 + 2 x 70 cm^2 + 2 x 63.6 cm^2
total surface area = 168 cm^2 + 140 cm^2 + 127.2 cm^2
total surface area = 435.2 cm^2

Therefore, the surface area of the rectangular pyramid is 435.2 cm^2.