To find the area of a trapezium (also known as a trapezoid in some regions), we use the formula:
[tex]\[
\text{Area} = \frac{1}{2} \times (a + b) \times h
\][/tex]
where:
- [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of the two parallel sides (bases) of the trapezium.
- [tex]\( h \)[/tex] is the height (the perpendicular distance between the two parallel sides).
Given the dimensions of the trapezium:
- [tex]\( a = 7 \, \text{cm} \)[/tex]
- [tex]\( b = 10.4 \, \text{cm} \)[/tex]
- [tex]\( h = 6.7 \, \text{cm} \)[/tex]
Let's plug these values into the formula:
[tex]\[
\text{Area} = \frac{1}{2} \times (7 + 10.4) \times 6.7
\][/tex]
First, add the lengths of the parallel sides:
[tex]\[
a + b = 7 + 10.4 = 17.4 \, \text{cm}
\][/tex]
Next, multiply this sum by the height:
[tex]\[
17.4 \times 6.7
\][/tex]
To calculate this product:
[tex]\[
17.4 \times 6.7 = 116.58 \, \text{cm}^2
\][/tex]
Finally, multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\text{Area} = \frac{1}{2} \times 116.58 = 58.29 \, \text{cm}^2
\][/tex]
So, the area of the trapezium is:
[tex]\[
\boxed{58.29 \, \text{cm}^2}
\][/tex]
