A rectangular piece of posterboard measures 60 centimeters by 80 centimeters. You draw a net of a box on the poster board and cut it out. If the box measures 10 centimeters by 16 centimeters by 27 centimeters, what is the area of the poster board left?
160 cm
To find the area of the poster board left, we need to subtract the area of the cut-out box from the total area of the poster board.
First, let's find the area of the poster board. The formula for finding the area of a rectangle is length × width.
Given that the length of the poster board is 60 centimeters and the width is 80 centimeters, we can calculate the area:
Area of the poster board = 60 cm × 80 cm = 4800 cm²
Next, let's find the surface area of the box. The surface area of a box is the sum of the areas of all its sides.
The box has six sides: two sides with dimensions 10 cm × 16 cm, two sides with dimensions 10 cm × 27 cm, and two sides with dimensions 16 cm × 27 cm.
Area of the box = 2 × (10 cm × 16 cm) + 2 × (10 cm × 27 cm) + 2 × (16 cm × 27 cm)
Area of the box = 320 cm² + 540 cm² + 864 cm²
Area of the box = 1724 cm²
Finally, to find the area of the poster board left, we subtract the area of the box from the total area of the poster board:
Area of the poster board left = Area of the poster board - Area of the box
Area of the poster board left = 4800 cm² - 1724 cm²
Area of the poster board left = 3076 cm²
Therefore, the area of the poster board left is 3076 cm².