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?
102,787.2 cm2
1,643.2 cm2
1,001.6 cm squared.
1,178.8 cm squared.
To find the surface area of a rectangular pyramid, we need to calculate the areas of the base and the four triangular faces.
The area of the rectangular base is:
Area = length * width
Area = 20 cm * 18 cm
Area = 360 cm²
The area of one triangular face (with base length 20 cm and height 16.6 cm) is:
Area = 0.5 * base * height
Area = 0.5 * 20 cm * 16.6 cm
Area = 166 cm²
The area of the other triangular face (with base length 18 cm and height 17.2 cm) is:
Area = 0.5 * base * height
Area = 0.5 * 18 cm * 17.2 cm
Area = 154.8 cm²
There are two of each triangular face, so the total area of the four triangular faces is:
Total area = 2*166 cm² + 2*154.8 cm²
Total area = 332 cm² + 309.6 cm²
Total area = 641.6 cm²
Finally, the total surface area of the rectangular pyramid is the sum of the base area and the four triangular faces:
Surface area = base area + total area of triangular faces
Surface area = 360 cm² + 641.6 cm²
Surface area = 1001.6 cm²
Therefore, the surface area of the rectangular pyramid is 1,001.6 cm².
So, the correct answer is 1,001.6 cm squared.