Subjects geometry

Area Trapezium

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Area Trapezium


1. **State the problem**: We want to find the area of a trapezium (trapezoid), which is a quadrilateral with exactly one pair of parallel sides. 2. **Identify the sides**: Let the lengths of the two parallel sides be $a$ and $b$, and the height (the perpendicular distance between the parallel sides) be $h$. 3. **Recall the formula**: The area $A$ of a trapezium is given by the formula $$ A = \frac{(a + b)}{2} \times h $$ 4. **Explanation**: This formula works because you essentially find the average length of the two parallel sides $(\frac{a+b}{2})$, then multiply by the height to get the total area. 5. **Example**: If $a=5$, $b=7$, and $h=4$, then $$ A = \frac{(5 + 7)}{2} \times 4 = \frac{12}{2} \times 4 = 6 \times 4 = 24 $$ So, the area is 24 square units.