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Answer :
Final Answer:
The surface area of the triangular prism is 45 cm².
Explanation:
Given dimensions:
Triangular base: Base = 5 cm, Height = 3 cm
Rectangular faces: 6 cm by 4 cm, 6 cm by 2 cm, and 6 cm by 3 cm
Calculation for the surface area:
Area of two triangular faces:
Area of one triangular face = (1/2) * base * height
Area of one triangular face= (1/2) * 5 cm * 3 cm = 7.5 square centimeters
Total area of both triangular faces = 2 * 7.5 = 15 square centimeters
Area of three rectangular faces:
First rectangular face area = 6 cm * 4 cm = 24 square centimeters
Second rectangular face area = 6 cm * 2 cm = 12 square centimeters
Third rectangular face area = 6 cm * 3 cm = 18 square centimeters
Total area of the three rectangular faces = 24 + 12 + 18 = 54 square centimeters
Sum up the areas of all faces:
Total surface area before adjustment = Total area of all faces = 15 square centimeters (triangular faces) + 54 square centimeters (rectangular faces) = 69 square centimeters
Adjustment for internal faces:
Subtract the area of the faces inside the prism from the total surface area: 69 square centimeters - 2 * (3 cm * 4 cm) = 69 square centimeters - 24 square centimeters = 45 square centimeters
Therefore, after considering the internal faces, the corrected surface area of the triangular prism is 45 square centimeters.
Nets provide a 2D representation of the 3D object's surfaces, allowing for easier visualization and calculation of its surface area. Nets are unfolded or flattened versions of 3D shapes, showcasing all the faces that comprise the solid object. They are helpful in understanding the structure and properties of various geometric figures.
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Complete Question
Using the net below, find the surface area of the triangular prism.
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The calculated surface area of the net is 82 square cm
Finding the surface area of the net
From the question, we have the following parameters that can be used in our computation:
The net of the triangular prism
The surface area of the net is then calculated as
Surface area = Area of rectangle + 2 * area of triangle
So, we have
Surface area = (3 + 4 + 5) * 6 + 2 * 1/2 * 5 * 2
Evaluate
Surface area = 82
Hence, the surface area of the net is 82 square cm
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