Question

Use the image to answer the question.

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 find the area of each face and then sum them up.

1. The area of the base:
Area = length x width
Area = 8 mm x 10 mm
Area = 80 mm²

2. The area of the four triangular faces:
a) The area of the face with a height of 12 mm:
Area = 1/2 x base x height = 1/2 x 8 mm x 12 mm = 48 mm²
b) The area of the face with a height of 15 mm:
Area = 1/2 x base x height = 1/2 x 10 mm x 15 mm = 75 mm²

3. Add up all the areas:
Surface Area = Base area + 4 x Triangular face area
Surface Area = 80 mm² + 4(48 mm² + 75 mm²)
Surface Area = 80 mm² + 4(123 mm²)
Surface Area = 80 mm² + 492 mm²
Surface Area = 572 mm²

Therefore, the surface area of the rectangular pyramid is 572 square millimeters.