Question

calculate the area of the trapezium/trapezoid shown.

Explanation:

Step1: Recall the formula for the area of a trapezoid

The formula for the area \( A \) of a trapezoid is \( A=\frac{(a + b)}{2}\times h \), where \( a \) and \( b \) are the lengths of the two parallel sides (bases) and \( h \) is the height (the perpendicular distance between the bases).

Step2: Identify the values of \( a \), \( b \), and \( h \)

From the diagram, the lengths of the two parallel sides are \( a = 12\space\text{mm} \) and \( b = 5\space\text{mm} \), and the height \( h = 7\space\text{mm} \) (note that the 6 mm is a non - parallel side, so we ignore it for the area calculation).

Step3: Substitute the values into the formula

Substitute \( a = 12 \), \( b = 5 \), and \( h = 7 \) into the formula:

$$
LATEXBLOCK0
$$

Answer:

The area of the trapezoid is \( 59.5\space\text{mm}^2 \)