Question

ABCD is a trapezium in which AB, CD, AD, DC, AB=20cm, BC=13cm, and DC=25cm. Find the area of the trapezium​.

a) 345 cm²
b) 625 cm²
c) 420 cm²
d) 520 cm²

Answer 1

To find the area of a trapezium, use the formula: Area = 0.5 × (sum of parallel sides) × height. Substitute the given values and calculate the area.

Step-by-step explanation:

To find the area of a trapezium, you can use the formula:

Area = 0.5 × (sum of parallel sides) × height

In the given trapezium, AB = 20cm, CD = 25cm, and BC = 13cm. The height is not given, so we need to find it using the Pythagorean theorem.

Using the Pythagorean theorem, we can find the height (AD) as follows:

AD² = AB² - BD²

AD² = 20² - BC²

AD² = 20² - 13²

AD² = 400 - 169

AD = √231

Now, we can substitute the values into the area formula:

Area = 0.5 × (20 + 25) × √231

Area ≈ 0.5 × 45 × 15.198

Area ≈ 342.915 cm²

Therefore, the area of the trapezium is approximately 342.915 cm²