Question

AB and DC are parallel sides of a trapezium ABCD and angle ADC is 90 degree given AB is 15cm, CD is40cm and diagonal AC is 41cm, calculate area of trapezium ABCD

Answer 1

In triangle ADC,
by Pythagoras theorem,
AC²=AD²+CD²
AD=√(41²-40²)
AD=√81
AD=9cm

the area of a trapezium= half× (sum of parallel sides)×height
so, the area =
$\frac{1}{2} \times (15 + 40) \times 9$
$= 287.5 {cm}^{2}$