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
1,643.2 cm2
1,643.2 cm squared
1,001.6 cm2
1,001.6 cm squared
102,787.2 cm2
102,787.2 cm squared
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To find the surface area of a rectangular pyramid, we need to calculate the area of the base and the area of the three triangular faces.
1. Area of the base:
Area = length * width
Area = 20 cm * 18 cm
Area = 360 cm^2
2. Area of the triangular faces:
Area = 1/2 * base * height
Area = 1/2 * 20 cm * 16.6 cm
Area = 166 cm^2 (x 2)
Total area of the two faces = 166 cm^2 + 166 cm^2 = 332 cm^2
Again,
Area = 1/2 * base * height
Area = 1/2 * 18 cm * 17.2 cm
Area = 154.8 cm^2
Total area of the two faces = 154.8 cm^2
Total surface area = Area of base + total area of the three triangular faces
Total surface area = 360 cm^2 + 332 cm^2 + 154.8 cm^2
Total surface area = 846.8 cm^2
Therefore, the surface area of the rectangular pyramid is 846.8 cm^2.
So, none of the provided options is correct.