A net of a triangular prism is shown below 10 10 6 6 8 3 what is the are in square centimeters of the triangular prism
To find the total surface area of a triangular prism, we need to find the individual areas of each face and add them together.
The triangular faces of the prism have dimensions 10, 10, 6 and 6. The area of a triangle can be calculated using Heron's formula:
s = (a + b + c) / 2
area = sqrt(s * (s - a) * (s - b) * (s - c))
For the first triangular face:
s1 = (10 + 10 + 6) / 2 = 13
area1 = sqrt(13 * (13 - 10) * (13 - 10) * (13 - 6)) = sqrt(13 * 3 * 3 * 7) = sqrt(819)
For the second triangular face:
s2 = (6 + 6 + 8) / 2 = 10
area2 = sqrt(10 * (10 - 6) * (10 - 6) * (10 - 8)) = sqrt(10 * 4 * 4 * 2) = sqrt(320)
The rectangular faces of the prism have dimensions 10, 8, and 3. The area of a rectangle is calculated by multiplying the length and width.
For the first rectangular face:
area3 = 10 * 8 = 80
For the second rectangular face:
area4 = 10 * 3 = 30
Adding up all the areas:
total area = area1 + area2 + area3 + area4 = sqrt(819) + sqrt(320) + 80 + 30 = approximately 9.44 + approximately 17.89 + 80 + 30 = approximately 137.33 square centimeters.
Therefore, the total surface area of the triangular prism is approximately 137.33 square centimeters.