To find the surface area of the prism, we first need to find the area of each of the five faces and then add them up.
1. Triangle face:
The base of the triangle is 6mm and the height can be found using Pythagorean theorem since the diagonal is given as 10mm. So, base = 6mm, height = sqrt(10^2 - 6^2) = sqrt(100 - 36) = sqrt(64) = 8mm. The area of the triangle is (1/2) * base * height = (1/2) * 6 * 8 = 24 sq mm.
2. Square face:
Top square: Area = side^2 = 7^2 = 49 sq mm.
Middle square: Area = side^2 = 8^2 = 64 sq mm.
Now, the surface area of the prism is the sum of the areas of all five faces:
Surface Area = 2(triangle faces) + 2(square faces) + 2(rectangular faces)
Surface Area = 2(24) + 2(49) + 2(64) = 48 + 98 + 128 = 274 sq mm
So, the surface area of the prism is 274 square millimeters.
Using the net of the prism shown, what is its surface area?
10 mm diagnal line of a triangle on the side
6mm bottom of a triangle on the side
7mm top square
8mm middle square
1 answer
1 answer