Question

What is the surface area of the figure above?

triangular prism one side is 3 cm the width is 4cm the front of the figure base is 6 cm and the other side is 5 cm and that side have a 90 degree angle

(1 point)
Responses

78 centimeters squared
78 centimeters squared

92 centimeters squared
92 centimeters squared

84 centimeters squared
84 centimeters squared

66 centimeters squared

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct answer is 78 centimeters squared.

To find the surface area of the triangular prism, we need to calculate the lateral area plus the area of the two triangular bases.

Lateral area:
1. Calculate the perimeter of the base triangle:
Perimeter = 3 + 4 + 5 = 12 cm

2. Calculate the height of the prism:
Height = 6 cm

3. Calculate the lateral area:
Lateral area = Perimeter x Height = 12 cm x 6 cm = 72 cm squared

Base area:
1. Calculate the area of one of the triangular bases:
Area = 0.5 x base x height
Area = 0.5 x 6 cm x 4 cm = 12 cm squared

2. Calculate the area of both bases:
2 x 12 cm squared = 24 cm squared

Total surface area = Lateral area + Base area = 72 cm squared + 24 cm squared = 96 cm squared