The area \( A \) of a trapezium is given by the formula:
\[ A = \frac{1}{2} \times \text{Sum of parallel sides} \times \text{Distance between parallel sides} \]
In this case, we know:
- The area \( A = 1100 \, \text{sqm} \)
- The distance between the two parallel sides \( h = 20 \, \text{m} \)
- One of the parallel sides \( b_1 = 70 \, \text{m} \)
We need to find the length of the other parallel side \( b_2 \).
Using the formula for the area of a trapezium, we have:
\[ 1100 = \frac{1}{2} \times (b_1 + b_2) \times 20 \]
Substitute the known values:
\[ 1100 = \frac{1}{2} \times (70 + b_2) \times 20 \]
Now, let's solve for \( b_2 \):
\[ 1100 = 10 \times (70 + b_2) \]
\[ 110 = 70 + b_2 \]
\[ b_2 = 110 - 70 \]
\[ b_2 = 40 \]
So, the length of the other parallel side is \( 40 \, \text{m} \).
Answer:
40m
Step-by-step explanation:
The distance between the two parallel sides is the height, which is 20 m. The are of a trapezium is A = h x (b1 + b2)/2, so we can find b2 by plugging in the values of 20m and 70m to get:
1100 = 20 x (70 + x)/2
1100 = (1400 + 20x)/2
1100 = 1400/2 + 20x/2
1100 = 700 + 10x
10x = 400
x = 40m
