Answer:To calculate the area of a trapezium, we need the lengths of its parallel sides (the bases) and the distance between them (the height). Given that the trapezium is not to scale, we assume the 10 cm, 9 cm, and 8 cm measurements refer to the lengths of the three sides.
Let's label the trapezium as ABCD, where AB is the longer base, CD is the shorter base, and AD and BC are the non-parallel sides.
Given:
AB = 10 cm (longer base)
CD = 8 cm (shorter base)
AD = 9 cm (non-parallel side)
To calculate the area of the trapezium, we can use the formula:
Area = (1/2) * (AB + CD) * height
However, the height is not given directly. We can calculate it using the Pythagorean theorem by considering triangle ADB.
Using the Pythagorean theorem, we have:
AD^2 = AB^2 - BD^2
Rearranging the equation to solve for BD:
BD^2 = AB^2 - AD^2
BD^2 = 10^2 - 9^2
BD^2 = 100 - 81
BD^2 = 19
BD = √19 cm (approx.)
Now that we have BD, we can use it as the height of the trapezium.
Area = (1/2) * (AB + CD) * height
Area = (1/2) * (10 + 8) * √19
Area = (1/2) * 18 * √19
Area = 9 * √19 cm² (approx.)
Therefore, the area of the trapezium is approximately 9√19 cm².
Explanation: