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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To find the surface area of the rectangular pyramid, we need to calculate the area of the four triangular faces and the area of the rectangular base, then add them together.
1. Area of the rectangular base:
Area = length x width
Area = 8mm x 10mm
Area = 80mm²
2. Area of the four triangular faces:
We have two triangles with base 8mm and height 12mm, and two triangles with base 10mm and height 15mm.
Area of a triangle = 0.5 x base x height
Area of the first two triangles = 0.5 x 8mm x 12mm = 48mm²
Area of the second two triangles = 0.5 x 10mm x 15mm = 75mm²
3. Total surface area:
Total surface area = 2 x sum of triangle areas + base area
Total surface area = 2(48mm² + 75mm²) + 80mm²
Total surface area = 2(123mm²) + 80mm²
Total surface area = 246mm² + 80mm²
Total surface area = 326mm²
Therefore, the surface area of the rectangular pyramid is 326mm².