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)
cm2
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
The base area can be calculated as the length times the width:
Base Area = 14 cm * 12 cm = 168 cm^2
The perimeter of the base can be calculated as 2 times the sum of the length and width:
Perimeter of Base = 2(14 cm + 12 cm) = 2(26 cm) = 52 cm
The slant height of the pyramid can be calculated using the Pythagorean theorem, as the hypotenuse of a right triangle with sides of 10 cm and 10.6 cm:
Slant Height = sqrt(10^2 + 10.6^2)
Slant Height = sqrt(100 + 112.36)
Slant Height = sqrt(212.36)
Slant Height ≈ 14.57 cm
Now we can plug these values into the formula:
Surface Area = 168 cm^2 + (1/2) * 52 cm * 14.57 cm
Surface Area = 168 cm^2 + 379.14 cm^2
Surface Area ≈ 547.14 cm^2
Therefore, the surface area of the rectangular pyramid is approximately 547.14 cm^2.