For this problem, we are given a composite figure made up of a rectangular prism and a triangular prism.
First, let's find the surface area of the rectangular prism:
The formula for the surface area of a rectangular prism is: 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
Given:
Length (l) = 6 units
Width (w) = 4 units
Height (h) = 5 units
Surface area of the rectangular prism = 2(6)(4) + 2(6)(5) + 2(4)(5)
Surface area of the rectangular prism = 48 + 60 + 40
Surface area of the rectangular prism = 148 square units
Next, let's find the surface area of the triangular prism:
The formula for the surface area of a triangular prism is: base area + lateral area, where base area is the area of the triangular base and lateral area is the perimeter of the base times the height of the prism.
Given:
Base of the triangle = 4 units
Height of the triangle = 5 units
Width of the prism = 4 units
Base area of the triangular prism = 1/2 * base * height
Base area of the triangular prism = 1/2 * 4 * 5
Base area of the triangular prism = 10 square units
Lateral area of the triangular prism = Perimeter of triangle * height of prism
Lateral area of the triangular prism = 3(4) * 4
Lateral area of the triangular prism = 12 * 4
Lateral area of the triangular prism = 48 square units
Surface area of the triangular prism = 10 + 48
Surface area of the triangular prism = 58 square units
Now, let's find the total surface area of the composite 3-D figure:
Total surface area = surface area of rectangular prism + surface area of triangular prism
Total surface area = 148 + 58
Total surface area = 206 square units
Therefore, the total surface area of the composite 3-D figure is 206 square units.
Surface area of composite 3-D figures practice 7B 6.23
1 answer
1 answer