Question

find the area of the trapezium whose parallel sides are 18 cm and 36 CM respectively and non parallel sides are equal and of 15 cm each

Answer 1

at first you have to divide the trapezium into a parallelogram ( dimensions : 18 cm and 15 cm) and an isoseles triangle ( dimensions: 15 cm,15cm, and 30cm - 18cm= 12 cm) .
Then draw a altitude ( form the vertex of the isoseles triangle which fall on the side 12 cm of the triangle ) . The altitude will divide the the base ( 12 cm) into 2 parts : 6 cm and 6 cm .
Then through Pythagoras theorem find out the height : √( (15)^2 - (6)^2) = √( 225-36 ) = √189
Then apply the formula to find out the area of trapezium :
1/2× ( sum of parrallel sides) × height
= 1/2 × ( 18 +30) × √189
= 1/2 × 48× √189
= 24× √189
Therefore the area of trapezium is 24√189