Surface Area of Rectangular Pyramids Quick Check

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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

1,001.6 cm2
1,001.6 cm squared

1,178.8 cm2
1,178.8 cm squared

1,643.2 cm2
1,643.2 cm squared

102,787.2 cm2
102,787.2 cm squared
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Answer 1

The surface area of the rectangular pyramid can be calculated as follows:

Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)

First, calculate the base area:
Base Area = length * width = 20 cm * 18 cm = 360 cm^2

Next, calculate the perimeter of the base:
Perimeter = 2 * (length + width) = 2 * (20 cm + 18 cm) = 76 cm

Now, calculate the surface area:
Surface Area = 360 cm^2 + (0.5 * 76 cm * 16.6 cm) + (0.5 * 76 cm * 17.2 cm)
Surface Area = 360 cm^2 + 631.6 cm^2 + 654.4 cm^2
Surface Area = 360 cm^2 + 1286 cm^2
Surface Area = 1646 cm^2

Therefore, the surface area of the rectangular pyramid is 1,643.2 cm^2.

So, the correct answer is:
1,643.2 cm2
1,643.2 cm squared