Question

Question

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An illustration shows a pyramid with a rectangular base. The length of the base is 8 millimeters and the width 10 millimeters. The perpendicular heights from the apex to the base length is 12 millimeters and to the base width is 15 millimeters. 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 area of the rectangular pyramid?

(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of the rectangular pyramid, we need to calculate the area of the base, the area of each lateral face, and then add them all together.

1. Area of the base:
Area = length x width
Area = 8 mm x 10 mm = 80 square mm

2. Area of each lateral face:
For the face with height 12 mm:
Area = (1/2) x base length x height
Area = (1/2) x 8 mm x 12 mm = 48 square mm

For the face with height 10 mm:
Area = (1/2) x base width x height
Area = (1/2) x 10 mm x 15 mm = 75 square mm

3. Total surface area:
Surface Area = 2 x Area of the base + Sum of areas of lateral faces
Surface Area = 2 x 80 square mm + 48 square mm + 75 square mm
Surface Area = 160 square mm + 123 square mm = 283 square mm

Therefore, the surface area of the rectangular pyramid is 283 square millimeters.