Use the image to answer the question.
An illustration shows a pyramid with a rectangular base. The length of the base is labeled 20 centimeters and the width as 18 centimeters. The perpendicular heights from the apex to the base length of 20 is 16.6 centimeters and to the base width of 18 is 17.2 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 of the rectangular pyramid?
(1 point)
Responses
1,178.8 cm2
1,178.8 cm squared
102,787.2 cm2
102,787.2 cm squared
1,001.6 cm2
1,001.6 cm squared
1,643.2 cm2
1,643.2 cm squared
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The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = base area + (perimeter of base x slant height)/2
The base area is the area of the rectangle: 20 cm x 18 cm = 360 cm^2
The perimeter of the base is 2(20 cm) + 2(18 cm) = 76 cm
The slant height for the 20 cm length is given as 16.6 cm, and for the 18 cm width is given as 17.2 cm.
Therefore, the surface area = 360 cm^2 + (76 cm x 16.6 cm)/2 + (76 cm x 17.2 cm)/2
Surface Area = 360 cm^2 + 632.8 cm^2 + 654.4 cm^2
Surface Area = 1,647.2 cm^2
Therefore, the surface area of the rectangular pyramid is 1,647.2 cm^2, which is closest to the answer 1,643.2 cm^2.