If a measures 12 cm, b measures 6 cm, and d measures 13 cm, what is the surface area of the rectangular pyramid?
It's not possible to find the surface area of the rectangular pyramid with just three measurements given. We need to know the height and the dimensions of the base in order to calculate the surface area.
To find the surface area of a rectangular pyramid, you need to calculate the areas of the different shapes that make up the surface.
1. First, find the area of the base of the pyramid. Since it is a rectangle, you can use the formula for the area of a rectangle: A = length x width.
The length of the base is a = 12 cm, and the width is b = 6 cm.
Area of the base = a x b = 12 cm x 6 cm = 72 cm².
2. Next, calculate the areas of the four triangular faces of the pyramid. Each triangular face has a base length equal to one side of the rectangle and a height equal to d, the height of the pyramid.
The base length of each triangular face is 6 cm, and the height of the pyramid is d = 13 cm.
Area of each triangular face = (base length x height) / 2.
Area of each triangular face = (6 cm x 13 cm) / 2 = 78 cm².
3. Since there are four triangular faces, the total area of the four faces is 4 times the area of one triangular face.
Total area of the four triangular faces = 4 x 78 cm² = 312 cm².
4. Finally, add the area of the base and the area of the four triangular faces to get the total surface area of the pyramid.
Total surface area = area of the base + total area of the four triangular faces.
Total surface area = 72 cm² + 312 cm² = 384 cm².
Therefore, the surface area of the rectangular pyramid is 384 cm².