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?
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = base area + (0.5 * perimeter of base * slant height)
First, calculate the base area:
Base area = length * width = 14 cm * 12 cm = 168 square cm
Next, calculate the perimeter of the base:
Perimeter of base = 2 * (length + width) = 2 * (14 cm + 12 cm) = 52 cm
Now, calculate the slant height of the pyramid:
Slant height can be calculated using the Pythagorean theorem:
slant height = √(10 cm)^2 + (10.6 cm)^2
slant height ≈ √(100 cm^2 + 112.36 cm^2) ≈ √212.36 cm^2 ≈ 14.58 cm
Now, plug the values into the formula and calculate the surface area:
Surface Area = 168 + (0.5 * 52 cm * 14.58 cm)
Surface Area = 168 + (0.5 * 757.76 cm^2)
Surface Area ≈ 168 + 378.88
Surface Area ≈ 546.88 square cm
Therefore, the surface area of the rectangular pyramid is approximately 546.88 square cm.