FINDING THE SURFACE AREA OF A COMPOSITE SOLID
About "Finding the surface area of a composite solid"
Finding the surface area of a composite solid :
A composite solid is made up of two or more solid figures.
To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.
Finding the surface area of a composite solid - Examples
Example 1 :
Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?
Solution :
Step 1 :
Identify the important information.
• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.
• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.
• One face of each prism is not on the surface of the figure.
Step 2 :
Find the surface area of each prism.
Add the areas. Subtract the areas of the parts not on the surface.
Step 3 :
Find the area of the triangular prism.
Perimeter = 17 + 17 + 30 = 64 cm
Base area = (1/2)(30)(8) = 120 sq.cm
Surface area = Ph + 2B
Surface area = 64(24) + 2(120)
Surface area = 1,776 sq.cm
Step 4 :
Find the area of the rectangular prism.
Perimeter = 2(30) + 2(24) = 108 cm
Base area = 30(24) = 720 sq.cm
Surface area = Ph + 2B
Surface area = 108(18) + 2(720)
Surface area = 3,384 sq.cm
Step 5 :
Add. Then subtract twice the areas of the parts not on the surface.
Surface area = 1,776 + 3,384 - 2(720) = 3,720 sq.cm
The surface area before the hole was drilled was 3,720 sq.cm.
