Determine the total surface area of the triangular prism.

Question

12cm 15cm 9cm 4cm

Answer 1

To find the total surface area of a triangular prism, we need to calculate the areas of all the faces and then add them up.

First, let's calculate the area of the two triangular faces:
Area of a triangle = 1/2 * base * height

Area of the first triangle = 1/2 * 12 cm * 15cm = 90 cm^2

Area of the second triangle = 1/2 * 9 cm * 15 cm = 67.5 cm^2

Next, let's calculate the area of the three rectangular faces:
Area of a rectangle = length * width

Area of the first rectangular face = 12 cm * 9 cm = 108 cm^2

Area of the second rectangular face = 12 cm * 4 cm = 48 cm^2

Area of the third rectangular face = 15 cm * 4 cm = 60 cm^2

Now, add up all the areas to find the total surface area of the triangular prism:
90 cm^2 + 67.5 cm^2 + 108 cm^2 + 48 cm^2 + 60 cm^2 = 373.5 cm^2

Therefore, the total surface area of the triangular prism is 373.5 cm^2.