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12. An alarm clock is shaped like a triangular prism. Each base of the clock is an equilateral triangle with the dimensions shown. 8cm 8cm Bcm The alarm clock has a height of 12 centimeters. What is the lateral surface area of the clock in square centimeters?

Respuesta :

Lateral surface area of a triangular prism

Initial explanation

We have the following clock:

We want to find the lateral surface area. This means all the area of the lateral faces (the rectangular faces).

In order to do so we find the perimeter of the triangle and then multiply it by 12 cm:

lateral area = perimeter x 12 cm

Finding the surface area

We have that the perimeter of the triangle is

8cm + 8 cm + 8 cm = 24 cm

Then the lateral area is

lateral area = perimeter x 12 cm

↓

lateral area = 24 cm x 12 cm

= 288 cm²

Then, the lateral surface area is 288 cm²

Answer: 288 cm²

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