Question

two parallel sides of a Trapezium are 58 cm and 42 CM the other two sides are of equal length which is 17 cm find the area of trapezium

Answer 1

Let ABCD is a trapezium in which AB parallel DC , AB = 58 cm , CD = 42 cm , BC = 17 cm and DA = 17 cm .

Draw DE Parallel BC and DL Perpendicular AB.

Then , DE = BC = 17 cm.

AE = ( AB - EB ) = ( 58 - CD ) = (58-42 ) = 16 cm.

In triangle DAE , we have :

a = AE = 16 cm , b = DE = 17 cm and c = DA = 17 cm.

Therefore,

Semi perimeter = 1/2 × ( 16 + 17 + 17 )

=> 1/2 × 50

=> 25 cm.

Area of triangle DAE = ✓s(s-a)(s-b)(s-c )

=> ✓25 × 9 × 8 × 8

=> √14400

=> 120 cm².

Also , Area of triangle DAE = 1/2 × AE × DL

=> ( 1/2 × 16 × DL) cm²

Therefore,

1/2 × 16 × DL = 120

DL = ( 120 × 2 ) / 16

DL = 15 cm.

Area of trapezium ABCD = { 1/2 × ( AB + DC ) × DL ) cm².

=> { 1/2 × ( 58 + 42 ) × 15 ) } cm²

=> 1/2 × 100 × 15 cm²

=> 750 cm².