Use the net as an aid to compute the surface area of the triangular prism.
Responses
A 192
192 m 2
B 216
216 m 2
C 240
240 m 2
D 300
the angles are 4m, 6m, 12m, and 5m
To calculate the surface area of a triangular prism, we need to find the area of the triangular bases and the three rectangular faces.
First, let's calculate the area of the triangular base:
Using Heron's formula to find the area of a triangle given the sides:
a = 4m
b = 6m
c = 5m
s = (a + b + c) / 2
s = (4 + 6 + 5) / 2
s = 15 / 2
s = 7.5
Area = √(s(s-a)(s-b)(s-c))
Area = √(7.5(7.5-4)(7.5-6)(7.5-5))
Area = √(7.5 * 3.5 * 1.5 * 2.5)
Area = √(91.875)
Area ≈ 9.58 m^2 (approx.)
The total area of the two triangular bases = 2 * 9.58 = 19.16 m^2
Now, let's calculate the area of the three rectangular faces:
The three sides of the triangular prism are 4m, 6m, and 12m.
The area of the three rectangular faces that make up the sides of the prism:
(4 * 6) + (6 * 12) + (4 * 12) = 24 + 72 + 48 = 144 m^2
Therefore, the total surface area of the triangular prism is:
Area of triangular bases + Area of rectangular faces = 19.16 + 144 = 163.16 m^2
Since none of the given options match the calculated surface area, it seems the given solution options are incorrect.