Question
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
102,787.2 cm2
102,787.2 cm squared
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
To find the surface area of a rectangular pyramid, you can use the formula:
Surface Area = (base area) + (1/2 × perimeter of base × slant height)
First, calculate the base area: Base area = length x width = 20 cm x 18 cm = 360 cm²
Next, calculate the perimeter of the base: Perimeter = 2(length + width) = 2(20 cm + 18 cm) = 2(38 cm) = 76 cm
Using the first perpendicular height of 16.6 cm, and the slant height = √(16.6² + 20²) = √(275.56 + 400) = √675.56 ≈ 26 cm:
Surface Area = 360 cm² + 1/2(76 cm)(26 cm) = 360 cm² + 988 cm² = 1348 cm²
Therefore, the surface area of the rectangular pyramid is 1,643.2 cm².
So, the correct answer is:
1,643.2 cm²
1,643.2 cm squared