An illustration shows a pyramid with a rectangular base. The length of the base is labeled 14 centimeters and the width as 12 centimeters. The perpendicular heights from the apex to the base length of 14 is 10 centimeters and to the base width of 12 is 10.6 centimeters. The perpendicular heights are denoted by two right angle symbols on two of the lateral faces from the apex to the base by dashed lines.
What is the surface area of the rectangular pyramid?
To find the surface area of the rectangular pyramid, we need to calculate the area of the base and the areas of the three congruent triangular faces.
1. Area of the base:
The area of the base is given by:
Area = length x width
Area = 14 cm x 12 cm
Area = 168 cm^2
2. Area of the triangular faces:
Each of the three triangular faces is a right triangle with base and height given by the dimensions of the base and the perpendicular height from the apex.
a) For the face with base length 14 cm:
Area = 0.5 x base x height
Area = 0.5 x 14 cm x 10 cm
Area = 70 cm^2
b) For the face with base width 12 cm:
Area = 0.5 x base x height
Area = 0.5 x 12 cm x 10.6 cm
Area = 63.6 cm^2
c) For the third face (which is identical in area to the first face):
Area = 70 cm^2
3. Total surface area:
Total surface area = Area of base + Area of three triangular faces
Total surface area = 168 cm^2 + 70 cm^2 + 63.6 cm^2 + 70 cm^2
Total surface area = 371.6 cm^2
Therefore, the surface area of the rectangular pyramid is 371.6 square centimeters.