the area of the trapezium is 21 cm².
To find the area of the trapezium, we can follow these steps:
1. Identify the missing dimension: We need to find the height of the trapezium.
2. Use the area of the triangle to find the height: We know the area of the triangle is 21 cm² and its base is 7 cm. We can use the formula for the area of a triangle:
Area of triangle = 1/2 * base * height
Solving for the height, we get:
height = area / (1/2 * base) = 21 cm² / (1/2 * 7 cm) = 6 cm
3. Calculate the area of the trapezium: Now that we have the height, we can use the formula for the area of a trapezium:
Area of trapezium = 1/2 * (sum of parallel bases) * height
The sum of the parallel bases is 5 cm + 2 cm = 7 cm. Therefore, the area of the trapezium is:
Area of trapezium = 1/2 * 7 cm * 6 cm = 21 cm²
Therefore, the area of the trapezium is 21 cm².