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?
To find the surface area of a rectangular pyramid, we need to calculate the area of the base and the area of the four triangular faces.
First, calculate the area of the base:
Area of base = length x width
Area of base = 8 mm x 10 mm
Area of base = 80 square mm
Next, calculate the area of the triangular faces:
There are four triangular faces in a rectangular pyramid, two with base length and two with base width.
1. Area of triangular face with base length:
Area = 1/2 x base x height
Area = 1/2 x 8 mm x 12 mm
Area = 48 square mm
2. Area of triangular face with base width:
Area = 1/2 x base x height
Area = 1/2 x 10 mm x 12 mm
Area = 60 square mm
Now, calculate the total surface area of the rectangular pyramid:
Surface area = Area of base + 2 x (Area of triangular face with base length) + 2 x (Area of triangular face with base width)
Surface area = 80 square mm + 2(48 square mm) + 2(60 square mm)
Surface area = 80 square mm + 96 square mm + 120 square mm
Surface area = 296 square mm
Therefore, the surface area of the rectangular pyramid is 296 square millimeters.