9514 1404 393
Answer:
- area = 211 +7√205 ≈ 311.22 square units
- volume = 273 cubic units
Step-by-step explanation:
Surface area
The length of the hypotenuse of the front facing triangle is given by the Pythagorean theorem:
d^2 = 13^2 +6^2 = 169 +36 = 205
d = √205
So, the perimeter of that triangle is ...
P = 13 +6 +√205 = 19 +√205
The total area of the rectangular faces of this triangular prism is then ...
rectangular face area = (base perimeter)·(prism height)
= (19 +√205)(7) = 133 +7√205
The area of the two triangular faces will be ...
triangular face total area = 2·(triangle area) = 2(1/2)(6)(13) = 78
Then the total surface area is ...
total surface area = rectangular face area + triangular face total area
total surface area = (133 +7√205) +78
surface area = 211 +7√205 ≈ 311.22 . . . . square units
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Volume
The volume is the product of the area of the triangular base and the height of the prism.
V = Bh
V = (39)(7)
volume = 273 . . . . cubic units
