Use the image to answer the question.
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?
(1 point)
To find the surface area of a rectangular pyramid, you need to calculate the area of the base and the area of the three triangular faces.
1. Area of the base:
Area = length x width = 14 cm x 12 cm = 168 square cm
2. Area of the three triangular faces:
For the face with a base length of 14 and height of 10, the area is:
1/2 x base x height = 1/2 x 14 cm x 10 cm = 70 square cm
For the face with a base width of 12 and height of 10.6, the area is:
1/2 x base x height = 1/2 x 12 cm x 10.6 cm = 63.6 square cm
Since a rectangular pyramid has four equal triangular faces, the total area of the three remaining triangular faces is 70 + 63.6 + 63.6 = 197.2 square cm.
3. Total surface area:
Surface area = base area + total area of all triangular faces
Surface area = 168 + 197.2 = 365.2 square cm
Therefore, the surface area of the rectangular pyramid is 365.2 square cm.