Question

pqrs is a trapezium with PQ parallel to RS and x and y are midpoints of non-parallel sides of trapezium if PQ is equal to 40 and Rs is equals to 10 then find xy​

Answer 1

Answer:172cm^2

Step-by-step explanation:

Triangles PQM and RSM are similar triangle as <PQM=<MSR----alternate angles.PQ is parallel to RS.

<PRS=MPQ —— same as noted above.

Both triangles are similar triangles.

Ratio of areas of similar triangles is square of their sides, heights etc.

So, 32 cm^2/50cm^2=16/25=4^2/5^2—-Ratio of their area is also square of their sides, heights etc.

Note the above statement

Common factor of ratio is 2.

Hence, PQ=8 cm and RS=10 cm, height of trapezium=18 cm.

Required area' x ‘of trapezium = 1/2*18*(8+10)=172 cm^2

Answer 2

Triangles PQM and RSM are similar triangle as

Both triangles are similar triangles.

Ratio of areas of similar triangles is square of their sides, heights etc.

So, 32 cm^2/50cm^2=16/25=4^2/5^2—-Ratio of their area is also square of their sides, heights etc.

Note the above statement

Common factor of ratio is 2.

Hence, PQ=8 cm and RS=10 cm, height of trapezium=18 cm.

Required area' x ‘of trapezium = 1/2*18*(8+10)=172 cm^2