Sara is making a model tent. How much material will she need? Explain the process to solve and show all calculations. The face of the object is 5cm and 5cm and 15cm. The edge of the shape is 3cm and 4cm.
To calculate the amount of material Sara will need, we need to find the surface area of the tent. In this case, the tent can be seen as a triangular prism with a triangular base and rectangular sides.
First, we calculate the area of the triangular base using the formula for the area of a triangle:
Base x Height / 2
In this case, the base is 5cm and the height is 15cm. So, the area of the triangular base is:
5cm x 15cm / 2 = 37.5cm²
Next, we calculate the area of the rectangular sides. Since there are two sides, we calculate the area of one side and then multiply by 2. The area of a rectangle is given by the formula:
Length x Width
For one side, the length is 15cm and the width is 4cm. So, the area of one side is:
15cm x 4cm = 60cm²
Multiplying this by 2 gives us the total area of the two sides:
60cm² x 2 = 120cm²
Now, we add the area of the triangular base and the two rectangular sides to get the total surface area of the tent:
37.5cm² (triangular base) + 120cm² (two rectangular sides) = 157.5cm²
Therefore, Sara will need 157.5cm² of material to make the model tent.