What is the surface area of the rectangular pyramid?
10.6m
10m
14m
12m
__cm2
To find the surface area of a rectangular pyramid, we need to calculate the area of the base and the area of each of the four triangular faces and then add them together.
First, let's calculate the area of the base:
Area of rectangle = length x width
Area of base = 10.6m x 10m = 106m²
Next, let's calculate the area of each triangular face. Since the base is a rectangle, the triangles will be right-angled triangles. To calculate the area of a right-angled triangle, we can use the formula:
Area of triangle = 0.5 x base x height
Given that the base of the triangle is 10.6m and the height of the triangle is 14m:
Area of each triangular face = 0.5 x 10.6m x 14m = 74.2m²
There are four triangular faces on a rectangular pyramid, so the total area of the four triangular faces is:
Total area of triangular faces = 4 x 74.2m² = 296.8m²
Now, we can find the total surface area of the rectangular pyramid by adding the area of the base and the area of the four triangular faces:
Total surface area = Area of base + Total area of triangular faces
Total surface area = 106m² + 296.8m² = 402.8m²
Therefore, the surface area of the rectangular pyramid is 402.8m².