Surface Area of Rectangular Pyramids Practice
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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)
mm2
To find the surface area of a rectangular pyramid, we first need to find the area of the base and the area of each of the four triangular faces.
1. Area of the base:
Area = length x width
Area = 8 mm x 10 mm
Area = 80 mm²
2. Area of each triangular face:
To find the area of a triangle, we use the formula: (1/2) x base x height
a. Triangular face with base 8 mm and height 12 mm:
Area = (1/2) x 8 mm x 12 mm
Area = 48 mm²
b. Triangular face with base 10 mm and height 12 mm:
Area = (1/2) x 10 mm x 12 mm
Area = 60 mm²
c. Triangular face with base 8 mm and height 15 mm:
Area = (1/2) x 8 mm x 15 mm
Area = 60 mm²
d. Triangular face with base 10 mm and height 15 mm:
Area = (1/2) x 10 mm x 15 mm
Area = 75 mm²
3. Total surface area:
Total surface area = area of the base + sum of the areas of the four triangular faces
Total surface area = 80 mm² + 48 mm² + 60 mm² + 60 mm² + 75 mm²
Total surface area = 323 mm²
Therefore, the surface area of the rectangular pyramid is 323 mm².