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
To find the surface area of a rectangular pyramid, we need to find the area of the rectangular base and each of the three triangular faces.
1. Area of the base:
Area = length * width
Area = 20 cm * 18 cm
Area = 360 cm²
2. Area of each triangular face:
A = 0.5 * base * height
Face 1: A = 0.5 * 20 cm * 16.6 cm
Face 1: A = 166 cm²
Face 2: A = 0.5 * 18 cm * 17.2 cm
Face 2: A = 154.8 cm²
Face 3: A = 0.5 * 20 cm * 17.2 cm
Face 3: A = 172 cm²
3. Total surface area:
Surface Area = Area of base + 3 * Area of triangular faces
Surface Area = 360 cm² + 3 * (166 cm² + 154.8 cm² + 172 cm²)
Surface Area = 360 cm² + 3 * 492.8 cm²
Surface Area = 360 cm² + 1478.4 cm²
Surface Area = 1838.4 cm²
Therefore, the surface area of the rectangular pyramid is 1838.4 cm².
one
The correct response is:
1,001.6 cm²