Question

Can’t you draw, trapeziums with the measurements given below?

(i) Parallel sides of length 7.5 centimetres and 5 centimetres; other two sides of length 6 centimetres and 5.5 centimetres.

(ii) Parallel sides of length 8 centimetres and 5.5 centimetres; angles on the longer side, 55° and 70°.

Answer 1

(i)

Let ABCD be the required trapezium.

Given: AB = 5 cm and DC = 7.5 cm

AD = 5.5 cm and BC = 6 cm.

Here is the rough sketch of the required trapezium.

The steps of construction are as follows:

(1) Draw a line segment DC of length 7.5 cm as the bottom side of the trapezium and then mark a point E at a distance of 7 cm − 5 cm = 2.5 cm from its right end such that EC is 2.5 cm long.

(2) Taking E and C as centres with radius 5.5 cm and 6 cm respectively, draw arcs intersecting each other at point B.

(3) Join EB and BC.

(4) Draw a line segment AB of length 5 cm parallel to the bottom line DC through the top vertex of the triangle ECB, using a set square.

(5) Join AD.

ABCD is the required trapezium.

(ii)

Let ABCD be the required trapezium.

Given: AB = 5.5 cm and DC = 8 cm

∠ADC = 55° and ∠BCD = 70°

Here is the rough sketch of the required trapezium.

The steps of construction are as follows:

(1) Draw a line segment DC of length 8 cm as the bottom side of the trapezium and then mark a point E at a distance of 8 cm − 5.5 cm = 2.5 cm from its right end such that EC is 2.5 cm long.

(2) At points D and C, draw ∠PDC and ∠RCD of measures 55° and 70° respectively.

(3) Draw a ray EQ parallel to DP at point E, which intersects the ray CR at point B.

(4) Draw a line segment from point B parallel to the bottom line DC which intersects the ray DP at point A, using a set square.

ABCD is the required trapezium.