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
1,001.6 cm2
1,001.6 cm squared
1,178.8 cm2
1,178.8 cm squared
102,787.2 cm2
102,787.2 cm squared
1,643.2 cm2
1,643.2 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 four triangles.
1. Area of the base:
Area of the base = length * width
Area of the base = 20 cm * 18 cm
Area of the base = 360 cm²
2. Area of the four triangles:
Area of one triangle = (1/2) * base * height
Area of one triangle = (1/2)(20 cm)(16.6 cm)
Area of one triangle = 166 cm²
Total area of the four triangles = 166 cm² * 4
Total area of the four triangles = 664 cm²
3. Adding the areas of the base and the four triangles:
Surface area = Area of the base + Total area of the four triangles
Surface area = 360 cm² + 664 cm²
Surface area = 1,024 cm²
Therefore, the surface area of the rectangular pyramid is 1,024 cm².
a) 1,001.6cm2
b) 1,178.8cm2
c) 102,787.2cm2
d) 1,643.2cm2
The correct answer is not among the options provided.
The correct surface area of the rectangular pyramid is 1,024 cm², as calculated in the previous response.
pick one that's provided
a) 1,001.6cm2
b) 1,178.8cm2
c) 102,787.2cm2
d) 1,643.2cm2
Based on the options provided:
The closest option to the correct surface area of the rectangular pyramid, which is 1,024 cm², is:
b) 1,178.8 cm²