A model of a wedge of cheese is used in a display for a deli. All the sides of the model are covered in yellow construction paper. A rectangular prism has a rectangular base with length of 15 centimeters and height of 5 centimeters. Another rectangle has length of 15 centimeters and height of 13 centimeters. Another rectangle has length of 15 centimeters, and height of 12 centimeters. The triangular sides have a base of 5 centimeters and heights of 12 centimeters. How much construction paper is needed for the model? 45 square cm 330 square cm 510 square cm 570 square cm

510 cm²

Step-by-step explanation:

To find how much construction paper is needed for the model, we calculate the total areas of each of its sides.

The area of the first triangular sides is A₁ = 15 cm × 5 cm = 75 cm²

The area of the second triangular sides is A₂ = 15 cm × 13 cm = 195 cm²

The area of the third triangular sides is A₃ = 15 cm × 12 cm = 180 cm²

The area of each triangular side is A₄ = 1/2 × 5 cm × 12 cm = 30 cm²

The area of the two triangular sides is A₅ = 2A₄ = 2 × 30 cm² = 60 cm²

The total surface area of a wedge of cheese is A = A₁ + A₂ + A₃ + A₅ = 75 cm² + 195 cm² + 180 cm² + 60 cm² = 510 cm²

So the amount of construction paper needed equals the total surface area of the wedge of cheese = 510 cm²