Sure, let's solve this step-by-step.
1. Understand the Problem: We know that 78 trapeziums together have a total of 312 sides. We need to determine how many sides 39 trapeziums would have.
2. Calculate Sides per Trapezium: First, we need to find out how many sides one trapezium has. We can do this by dividing the total number of sides by the number of trapeziums.
[tex]\[
\text{Sides per trapezium} = \frac{\text{Total sides}}{\text{Number of trapeziums}} = \frac{312}{78}
\][/tex]
Dividing 312 by 78, we get 4. Thus, each trapezium has 4 sides.
3. Calculate Total Sides for 39 Trapeziums: Now that we know each trapezium has 4 sides, we can find the total number of sides for 39 trapeziums by multiplying the number of sides per trapezium by the number of trapeziums.
[tex]\[
\text{Total sides for 39 trapeziums} = \text{Sides per trapezium} \times \text{Number of trapeziums} = 4 \times 39
\][/tex]
Multiplying 4 by 39, we get 156.
Therefore, 39 trapeziums will have a total of 156 sides.
