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)
mm2
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give correct answer
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = 0.5 * (base perimeter * slant height) + base area
First, calculate the base perimeter:
Perimeter = 2(length + width)
Perimeter = 2(8 + 10)
Perimeter = 2(18)
Perimeter = 36 mm
Next, calculate the slant height:
Slant height = √(height^2 + (0.5 * base perimeter)^2)
Slant height = √(12^2 + 18^2)
Slant height = √(144 + 324)
Slant height = √468
Slant height ≈ 21.63 mm
Now, calculate the surface area:
Surface Area = 0.5 * (36 * 21.63) + (8 * 10)
Surface Area = 0.5 * (777.48) + 80
Surface Area = 388.74 + 80
Surface Area = 468.74 mm2
Therefore, the surface area of the rectangular pyramid is 468.74 mm2.