Surface Area of Rectangular Pyramids Practice
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?
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To find the surface area of a rectangular pyramid, we need to calculate the area of each of its components and add them together.
1. Base Area:
The area of the rectangular base can be calculated as:
Area = length x width
Area = 8 mm x 10 mm
Area = 80 mm^2
2. Lateral Faces Area:
To calculate the area of the two triangular faces, we can use the formula for the area of a triangle:
Area = 1/2 x base x height
For the face with base length 8 mm and height 12 mm:
Area = 1/2 x 8 mm x 12 mm
Area = 48 mm^2
For the face with base length 10 mm and height 15 mm:
Area = 1/2 x 10 mm x 15 mm
Area = 75 mm^2
Adding the areas of the two triangular faces:
Total lateral faces area = 48 mm^2 + 75 mm^2
Total lateral faces area = 123 mm^2
3. Total Surface Area:
To find the total surface area of the pyramid, we add the base area and the total lateral faces area:
Total surface area = Base Area + Total lateral faces area
Total surface area = 80 mm^2 + 123 mm^2
Total surface area = 203 mm^2
Therefore, the surface area of the rectangular pyramid is 203 mm^2.